## 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 |
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babytarazkp | 0 | 6,046,146,456 | 100% | ||
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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% | ||
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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% | ||
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toni.pal | 0 | 0 | 0.6% |
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author | hivebuzz |
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permlink | hivebuzz-notify-quantumdeveloper-20201024t194332000z |
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author | mapxv |
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permlink | re-math-contest-27-results-and-solution-20200108t191643z |
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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 |
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author | stem.curate |
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permlink | q3t4qt |
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author | trendotoken |
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