## 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 |
|---|---|
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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 |
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| author | mapxv |
|---|---|
| permlink | re-math-contest-27-results-and-solution-20200108t191643z |
| category | puzzle |
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|---|---|
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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 |
|---|---|
| permlink | q3t4qt |
| category | puzzle |
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|---|---|
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hiveblocks