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

Tags were heavily modified to better represent problems.

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Found problems: 2

2010 Laurențiu Panaitopol, Tulcea, 2
Tags: freshman s dream , frobenius , nilpotence
Let be two $ n\times n $ complex matrices $ A,B $ satisfying the equations $ (A+B)^2=A^2+B^2 $ and $ (A+B)^4=A^4+B^4. $ Show that $ (AB)^2=0. $

2004 Alexandru Myller, 1
Tags: number theory , abstract algebra , field theory , ring theory , freshman s dream
Show that the equation $ (x+y)^{-1}=x^{-1}+y^{-1} $ has a solution in the field of integers modulo $ p $ if and only if $ p $ is a prime congruent to $ 1 $ modulo $ 3. $ [i]Mihai Piticari[/i]