A Problem in Number Theory

For discussing Olympiad Level Number Theory problems
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Kazi_Zareer
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A Problem in Number Theory

Unread post by Kazi_Zareer » Sun Jan 03, 2016 1:38 am

দেখাও যে, যেকোনো মৌলিক সংখ্যা $p$ এর জন্য এমন অসীম সংখ্যক পূর্ণসংখ্যা $a$ আছে অথবা একটিও নেই যেন $6p| a^{p}+1$

"Impossible only means that you haven't found the solution yet."
We cannot solve our problems with the same thinking we used when we create them.

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Phlembac Adib Hasan
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Re: A Problem in Number Theory

Unread post by Phlembac Adib Hasan » Sun Jan 03, 2016 11:21 am

For odd $p$, consider $a=6pk-1$ for $k\in\mathbb N$
For even $p$, note that $4\not | a^2+1$, where $a\in \mathbb Z$
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Naheed
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Re: A Problem in Number Theory

Unread post by Naheed » Thu Jan 28, 2016 12:00 pm

I don't get you Adib.

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