This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 2

2007 Nicolae Coculescu, 4
Tags: totient , euler , divisibility , number theory
Prove that $ p $ divides $ \varphi (1+a^p) , $ where $ a\ge 2 $ is a natural number, $ p $ is a prime, and $ \varphi $ is Euler's totient. [i]Cristinel Mortici[/i]

2010 N.N. Mihăileanu Individual, 4
Tags: totient , ring theory , modular arithmetic , abstract algebra
If $ p $ is an odd prime, then the following characterization holds. $$ 2^{p-1}\equiv 1\pmod{p^2}\iff \sum_{2=q}^{(p-1)/2} q^{p-2}\equiv -1\pmod p $$ [i]Marius Cavachi[/i]