## Solution The problem of this contest was to proof an equivalence:  I also just noticed that this inequation only holds for uneven, positive values of n(which is probably the reason why I had no entries this week). First of all a small explanation why this is even true: if x is bigger than 0: Then 1/x^n is only < 1 if x > 1. if x is smaller 0: Then 1/x^n is only < -1 if x > -1 These two cases connect both inequations. In this case you can rearrange the leftern inequation to: `1 < x^(n+1) if x > 0` → `x > 1` `1 > x^(n+1) if x < 0` → `1 > ±x` → `-1 < ±x` → `-1 < x` The ± comes from taking an even root. So if x > 0 than x > 1 is the only solution and if x < 0, x > -1 is the only solution. Putting the 2 together gets the rightern side of the equivalence: `x > 1` or `-1 < x < 0` And the way back to prove it actually is an equivalence: `x > 1` → `x^(n+1) > 1` → `x > 1/x^n` `-1 < x < 0` → `1 < x^(n+1)` → `x > 1/x^n` *↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓* ### List of participants with their entries: Name | solution found | comment - | - | - @tonimontana | none | found one of the errors I made → you get the reward *↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓* ## Winner draw: Not necessary since only 1 participant: Congratulations @tonimontana , you won 2 SBI! *↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓* ### The next contest starts soon. Don't miss it! ### This contest will continue as a 2-week contest as it's getting harder to find a unique problem and I have more stress lately.
| author | quantumdeveloper |
|---|---|
| permlink | math-contest-27-results-and-solution |
| category | puzzle |
| json_metadata | {"tags":["puzzle","contest","steembasicincome","stem","math","mathematics","steemstem","sbi","steemiteducation","palnet"],"users":["tonimontana"],"image":["https://steemitimages.com/p/NTy4GV6ooFRkjTArCrebYc2WCCmX2KY4SfTbUDpHWg6ZYGGDQxkSJMEeDstbGRGui2ebEURsduenEkUUxQ1WAp1yvfxKEXKyyX4zMKofsf5yNW7Pd9n6zTpc6CpRwT9kgr9wTfq9tgpfHYz7DKGgQ1sUYSTA6e52k49nouuG?format=match&mode=fit&width=640"],"app":"palnet/0.1","format":"markdown","canonical_url":"undefined/@quantumdeveloper/math-contest-27-results-and-solution"} |
| created | 2020-01-08 18:41:21 |
| last_update | 2020-01-08 18:41:21 |
| depth | 0 |
| children | 7 |
| last_payout | 2020-01-15 18:41:21 |
| cashout_time | 1969-12-31 23:59:59 |
| total_payout_value | 0.143 HBD |
| curator_payout_value | 0.136 HBD |
| pending_payout_value | 0.000 HBD |
| promoted | 0.000 HBD |
| body_length | 1,759 |
| author_reputation | 4,456,611,502,865 |
| root_title | "Math Contest #27 Results and Solution" |
| beneficiaries | [] |
| max_accepted_payout | 1,000,000.000 HBD |
| percent_hbd | 10,000 |
| post_id | 94,195,322 |
| net_rshares | 1,529,805,794,679 |
| author_curate_reward | "" |
| voter | weight | wgt% | rshares | pct | time |
|---|---|---|---|---|---|
| slider2990 | 0 | 8,675,165,309 | 100% | ||
| techken | 0 | 0 | 0.2% | ||
| edkarnie | 0 | 81,408,900,012 | 20% | ||
| crokkon | 0 | 58,596,888,995 | 100% | ||
| steembasicincome | 0 | 321,432,408,719 | 4.65% | ||
| mmmmkkkk311 | 0 | -669,123,595,818 | -10% | ||
| bengy | 0 | 23,319,671,318 | 20% | ||
| raise-me-up | 0 | 0 | 0.01% | ||
| tonimontana | 0 | 780,860,047 | 22.63% | ||
| nin4i | 0 | 557,609,466 | 100% | ||
| zuerich | 0 | 411,670,862,455 | 30% | ||
| skylinebuds | 0 | 881,356,210 | 2% | ||
| gordonramzy | 0 | 13,710,337,954 | 100% | ||
| jessica.steem | 0 | 13,387,391,191 | 100% | ||
| remlaps-lite | 0 | 0 | 100% | ||
| laissez-faire | 0 | 47,330,723 | 100% | ||
| darklands | 0 | 115,594,583,468 | 58% | ||
| driveforkids | 0 | 33,086,267,180 | 40% | ||
| limka | 0 | 0 | 1% | ||
| sonomori609 | 0 | 1,036,920,473 | 100% | ||
| bewithbreath | 0 | 738,217,551 | 2.32% | ||
| paolo.senegal | 0 | 14,566,022,735 | 100% | ||
| brendanweinhold | 0 | 57,912,099 | 100% | ||
| onespringday | 0 | 1,369,631,953 | 10% | ||
| quantumdeveloper | 0 | 2,523,722,103 | 50% | ||
| maruskina | 0 | 14,381,598,817 | 50% | ||
| nalacanecorso | 0 | 1,251,257,607 | 100% | ||
| budwizard | 0 | 0 | 1% | ||
| onecent | 0 | 1,394,546,716 | 22% | ||
| babytarazkp | 0 | 6,046,146,456 | 100% | ||
| trendovoter | 0 | 76,198,808,403 | 47.18% | ||
| mapxv | 0 | 41,616,668,535 | 4.59% | ||
| abh12345.stem | 0 | 564,096,307 | 50% | ||
| sbi-tokens | 0 | 67,691,553 | 1.51% | ||
| btc4breackfast | 0 | 15,941,118,869 | 100% | ||
| giphy | 0 | 3,187,960,016 | 10% | ||
| brustem | 0 | 347,335,604 | 100% | ||
| curation.stem | 0 | 0 | 75% | ||
| mk-pal-token | 0 | -279,414,273 | -10% | ||
| mk-sports-token | 0 | -615,437,346 | -10% | ||
| mk-gg-token | 0 | -346,781,054 | -10% | ||
| mk-marlians-tkn | 0 | -330,964,402 | -10% | ||
| untersatz | 0 | 57,012,468,018 | 10% | ||
| mk-photo-token | 0 | -544,847,482 | -10% | ||
| stem.alfa | 0 | 489,379,081 | 100% | ||
| alby2 | 0 | 16,665,773,342 | 100% | ||
| vxc.stem | 0 | 37,473,038 | 100% | ||
| yggdrasil.laguna | 0 | 327,472,891 | 70% | ||
| riccc96 | 0 | 34,021,971,815 | 100% | ||
| cd-stem | 0 | 542,913,606 | 100% | ||
| pecoshop | 0 | 1,622,709,797 | 100% | ||
| dzimfalase | 0 | -9,002,601 | -10% | ||
| culkio | 0 | -5,343,950 | -10% | ||
| miti.stem | 0 | 327,530,563 | 100% | ||
| stem.curate | 0 | 40,280,865,487 | 100% | ||
| stemisaria | 0 | 1,783,528,268 | 100% | ||
| hjmarseille | 0 | 9,249,437,725 | 70% | ||
| boomalex | 0 | 682,765,079,142 | 100% | ||
| updooter | 0 | 84,043,852,948 | 100% | ||
| ilovemk311 | 0 | 1,359,015,288 | 50% | ||
| dolcesalato1981 | 0 | 574,128,859 | 80% | ||
| machete9595 | 0 | 5,518,292,893 | 100% | ||
| toni.pal | 0 | 0 | 0.6% |
Congratulations @quantumdeveloper! You have completed the following achievement on the Hive blockchain and have been rewarded with new badge(s) : <table><tr><td><img src="https://images.hive.blog/60x70/http://hivebuzz.me/@quantumdeveloper/upvotes.png?202010241912"></td><td>You distributed more than 3000 upvotes. Your next target is to reach 4000 upvotes.</td></tr> </table> <sub>_You can view your badges on [your board](https://hivebuzz.me/@quantumdeveloper) and compare yourself to others in the [Ranking](https://hivebuzz.me/ranking)_</sub> <sub>_If you no longer want to receive notifications, reply to this comment with the word_ `STOP`</sub> **Do not miss the last post from @hivebuzz:** <table><tr><td><a href="/hivebuzz/@hivebuzz/papilloncharity"><img src="https://images.hive.blog/64x128/https://i.imgur.com/AL9FW96.png"></a></td><td><a href="/hivebuzz/@hivebuzz/papilloncharity">Hivebuzz support the Papillon Foundation Charity project</a></td></tr><tr><td><a href="/hive-120078/@hivebuzz/october-2020-is-the-world-mental-heath-month"><img src="https://images.hive.blog/64x128/https://i.imgur.com/GWiQc2h.png"></a></td><td><a href="/hive-120078/@hivebuzz/october-2020-is-the-world-mental-heath-month">October 2020 is the World Mental Heath Month</a></td></tr></table>
| author | hivebuzz |
|---|---|
| permlink | hivebuzz-notify-quantumdeveloper-20201024t194332000z |
| category | puzzle |
| json_metadata | {"image":["http://hivebuzz.me/notify.t6.png"]} |
| created | 2020-10-24 19:43:30 |
| last_update | 2020-10-24 19:43:30 |
| depth | 1 |
| children | 0 |
| last_payout | 2020-10-31 19:43:30 |
| cashout_time | 1969-12-31 23:59:59 |
| total_payout_value | 0.000 HBD |
| curator_payout_value | 0.000 HBD |
| pending_payout_value | 0.000 HBD |
| promoted | 0.000 HBD |
| body_length | 1,284 |
| author_reputation | 369,402,100,587,838 |
| root_title | "Math Contest #27 Results and Solution" |
| beneficiaries | [] |
| max_accepted_payout | 1,000,000.000 HBD |
| percent_hbd | 10,000 |
| post_id | 100,237,357 |
| net_rshares | 0 |
A member bonus $trendotoken tip, and !trendovoter, for @quantumdeveloper from MAPXV! These bonuses are for members, selected at random, and last for a few days. Win MAPR tokens in this new [Nonsense Writing Contest](https://steemit.com/hive-138861/@rycharde/new-nonsense-writing-contest-prizes-worth-over-30-steem-ends-sun-12-jan). Also consider our [MAPR fund](https://steem-engine.com/?p=market&t=MAPR) and [MAXUV](https://steem-engine.com/?p=market&t=MAXUV) vote bonds too. MAP Steem Fintech: growing your STEEM without SP.
| author | mapxv |
|---|---|
| permlink | re-math-contest-27-results-and-solution-20200108t191643z |
| category | puzzle |
| json_metadata | "{"app": "rewarding/0.1.5"}" |
| created | 2020-01-08 19:16:45 |
| last_update | 2020-01-08 19:16:45 |
| depth | 1 |
| children | 1 |
| last_payout | 2020-01-15 19:16:45 |
| cashout_time | 1969-12-31 23:59:59 |
| total_payout_value | 0.000 HBD |
| curator_payout_value | 0.000 HBD |
| pending_payout_value | 0.000 HBD |
| promoted | 0.000 HBD |
| body_length | 532 |
| author_reputation | 9,809,854,088,378 |
| root_title | "Math Contest #27 Results and Solution" |
| beneficiaries | [] |
| max_accepted_payout | 1,000,000.000 HBD |
| percent_hbd | 10,000 |
| post_id | 94,196,374 |
| net_rshares | 0 |
Congratulations @mapxv, you successfuly trended the post shared by @quantumdeveloper! @quantumdeveloper will receive <b>4.97891813</b> [TRDO](https://steem-engine.com/?p=history&t=TRDO) & @mapxv will get <b>3.31927875</b> [TRDO](https://steem-engine.com/?p=history&t=TRDO) curation in 3 Days from Post Created Date! <b>"Call [TRDO](https://steem-engine.com/?p=history&t=TRDO), Your Comment Worth Something!"</b> --- <sup>To view or trade TRDO go to [steem-engine.com](https://steem-engine.com/?p=market&t=TRDO) Join [TRDO Discord Channel](https://discord.gg/wySP8T9) or Join [TRDO Web Site](http://www.trendotoken.info/)</sup>
| author | trendotoken |
|---|---|
| permlink | re-mapxv-re-math-contest-27-results-and-solution-20200108t191643z-20200108t191653719z |
| category | puzzle |
| json_metadata | {"tags":["comments-scot","trendo-bot"],"app":"comments-scot/1.1","format":"markdown"} |
| created | 2020-01-08 19:16:54 |
| last_update | 2020-01-08 19:16:54 |
| depth | 2 |
| children | 0 |
| last_payout | 2020-01-15 19:16:54 |
| cashout_time | 1969-12-31 23:59:59 |
| total_payout_value | 0.000 HBD |
| curator_payout_value | 0.000 HBD |
| pending_payout_value | 0.000 HBD |
| promoted | 0.000 HBD |
| body_length | 628 |
| author_reputation | 5,546,209,053,433 |
| root_title | "Math Contest #27 Results and Solution" |
| beneficiaries | [] |
| max_accepted_payout | 1,000,000.000 HBD |
| percent_hbd | 10,000 |
| post_id | 94,196,379 |
| net_rshares | 0 |
Congratulations @quantumdeveloper! You have completed the following achievement on the Steem blockchain and have been rewarded with new badge(s) : <table><tr><td><img src="https://steemitimages.com/60x70/http://steemitboard.com/@quantumdeveloper/votes.png?202001181956"></td><td>You distributed more than 2000 upvotes. Your next target is to reach 3000 upvotes.</td></tr> </table> <sub>_You can view [your badges on your Steem Board](https://steemitboard.com/@quantumdeveloper) and compare to others on the [Steem Ranking](https://steemitboard.com/ranking/index.php?name=quantumdeveloper)_</sub> <sub>_If you no longer want to receive notifications, reply to this comment with the word_ `STOP`</sub> > You can upvote this notification to help all Steem users. Learn how [here](https://steemit.com/steemitboard/@steemitboard/http-i-cubeupload-com-7ciqeo-png)!
| author | steemitboard |
|---|---|
| permlink | steemitboard-notify-quantumdeveloper-20200118t203744000z |
| category | puzzle |
| json_metadata | {"image":["https://steemitboard.com/img/notify.png"]} |
| created | 2020-01-18 20:37:42 |
| last_update | 2020-01-18 20:37:42 |
| depth | 1 |
| children | 0 |
| last_payout | 2020-01-25 20:37:42 |
| cashout_time | 1969-12-31 23:59:59 |
| total_payout_value | 0.000 HBD |
| curator_payout_value | 0.000 HBD |
| pending_payout_value | 0.000 HBD |
| promoted | 0.000 HBD |
| body_length | 863 |
| author_reputation | 38,975,615,169,260 |
| root_title | "Math Contest #27 Results and Solution" |
| beneficiaries | [] |
| max_accepted_payout | 1,000,000.000 HBD |
| percent_hbd | 10,000 |
| post_id | 94,522,469 |
| net_rshares | 0 |
Hello, Your post has been manually curated by a @stem.curate curator. <center></center><center> Supporting Steemians on STEMGeeks</center> We are dedicated to supporting great content, like yours on the [STEMGeeks](stemgeeks.net) tribe. Please join us on [discord](https://discord.gg/73WaANa).
| author | stem.curate |
|---|---|
| permlink | q3t4qt |
| category | puzzle |
| json_metadata | {"tags":["puzzle","stem"],"users":["stem.curate"],"image":["https://cdn.steemitimages.com/DQmaqMpaEpJBAwJMN9bCHhmTzUEuymBj8V4BMsiJteZMG7L/FA8866FD-F2C3-43B3-A5A5-E0324BA4BB47.jpeg"],"links":["stemgeeks.net","https://discord.gg/73WaANa"],"app":"stemgeeks/0.1","canonical_url":"https://stemgeeks.net/@stem.curate/q3t4qt"} |
| created | 2020-01-08 21:23:21 |
| last_update | 2020-01-08 21:23:21 |
| depth | 1 |
| children | 0 |
| last_payout | 2020-01-15 21:23:21 |
| cashout_time | 1969-12-31 23:59:59 |
| total_payout_value | 0.000 HBD |
| curator_payout_value | 0.000 HBD |
| pending_payout_value | 0.000 HBD |
| promoted | 0.000 HBD |
| body_length | 462 |
| author_reputation | 599,563,679,404 |
| root_title | "Math Contest #27 Results and Solution" |
| beneficiaries | [] |
| max_accepted_payout | 1,000,000.000 HBD |
| percent_hbd | 10,000 |
| post_id | 94,199,774 |
| net_rshares | 0 |
Congratulations @quantumdeveloper, your post successfully recieved <b>4.97891813</b> [TRDO](https://steem-engine.com/?p=history&t=TRDO) from below listed TRENDO callers:<br> > <sup>@mapxv earned : **3.31927875** [TRDO](https://steem-engine.com/?p=history&t=TRDO) curation</sup> --- <sup>To view or trade TRDO go to [steem-engine.com](https://steem-engine.com/?p=market&t=TRDO) Join [TRDO Discord Channel](https://discord.gg/wySP8T9) or Join [TRDO Web Site](http://www.trendotoken.info/)</sup>
| author | trendotoken |
|---|---|
| permlink | re-quantumdeveloper-math-contest-27-results-and-solution-20200111t191806279z |
| category | puzzle |
| json_metadata | {"tags":["trdo","trendo-bot"],"app":"comments-scot/1.1","format":"markdown"} |
| created | 2020-01-11 19:18:09 |
| last_update | 2020-01-11 19:18:09 |
| depth | 1 |
| children | 0 |
| last_payout | 2020-01-18 19:18:09 |
| cashout_time | 1969-12-31 23:59:59 |
| total_payout_value | 0.000 HBD |
| curator_payout_value | 0.000 HBD |
| pending_payout_value | 0.000 HBD |
| promoted | 0.000 HBD |
| body_length | 495 |
| author_reputation | 5,546,209,053,433 |
| root_title | "Math Contest #27 Results and Solution" |
| beneficiaries | [] |
| max_accepted_payout | 1,000,000.000 HBD |
| percent_hbd | 10,000 |
| post_id | 94,303,960 |
| net_rshares | 0 |
Congratulations @mapxv, <b>47.18%</b> upvote has been shared with your successful call on the post that shared by @quantumdeveloper! --- <sup>Support <b>@trendotoken</b> projects by delegating : <b>[100SP](https://beta.steemconnect.com/sign/delegateVestingShares?delegator=YOURUSERNAME&delegatee=trendovoter&vesting_shares=100.000%20SP)</b> , <b>[200SP](https://beta.steemconnect.com/sign/delegateVestingShares?delegator=YOURUSERNAME&delegatee=trendovoter&vesting_shares=200.000%20SP) , <b>[500SP](https://beta.steemconnect.com/sign/delegateVestingShares?delegator=YOURUSERNAME&delegatee=trendovoter&vesting_shares=500.000%20SP)</b> , <b>[1000SP](https://beta.steemconnect.com/sign/delegateVestingShares?delegator=YOURUSERNAME&delegatee=trendovoter&vesting_shares=1000.000%20SP)</b> , <b>[2000SP](https://beta.steemconnect.com/sign/delegateVestingShares?delegator=YOURUSERNAME&delegatee=trendovoter&vesting_shares=2000.000%20SP)</b></sup>
| author | trendovoter |
|---|---|
| permlink | re-quantumdeveloper-math-contest-27-results-and-solution-20200108t191653933z |
| category | puzzle |
| json_metadata | {"tags":["trdo","newsteem"],"app":"trdo-voter/1.0","format":"markdown"} |
| created | 2020-01-08 19:16:54 |
| last_update | 2020-01-08 19:16:54 |
| depth | 1 |
| children | 0 |
| last_payout | 2020-01-15 19:16:54 |
| cashout_time | 1969-12-31 23:59:59 |
| total_payout_value | 0.000 HBD |
| curator_payout_value | 0.000 HBD |
| pending_payout_value | 0.000 HBD |
| promoted | 0.000 HBD |
| body_length | 944 |
| author_reputation | 58,041,103,589 |
| root_title | "Math Contest #27 Results and Solution" |
| beneficiaries | [] |
| max_accepted_payout | 1,000,000.000 HBD |
| percent_hbd | 10,000 |
| post_id | 94,196,381 |
| net_rshares | 0 |
hiveblocks