- Thread starter
- Moderator
- #1
- Jan 26, 2012
- 995
Thanks to those who participated in last week's POTW!! Here's this week's problem!
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Problem: Show that $n^{13}-n$ is divisible by $2730$ for all $n$.
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Note: This is equivalent to showing that $n^{13}-n\equiv 0\pmod{2730}$ for all $n$.
Hint:
Remember to read the POTW submission guidelines to find out how to submit your answers!
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Problem: Show that $n^{13}-n$ is divisible by $2730$ for all $n$.
-----
Note: This is equivalent to showing that $n^{13}-n\equiv 0\pmod{2730}$ for all $n$.
Hint:
Use Fermat's theorem coupled with the Chinese Remainder Theorem to show this result.
Remember to read the POTW submission guidelines to find out how to submit your answers!