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Putnam 2012 B6

Source:

December 3, 2012
Putnammodular arithmeticEulerquadraticsalgebrapolynomiallinear algebra

Problem Statement

Let pp be an odd prime number such that p≡2(mod3).p\equiv 2\pmod{3}. Define a permutation π\pi of the residue classes modulo pp by π(x)≡x3(modp).\pi(x)\equiv x^3\pmod{p}. Show that π\pi is an even permutation if and only if p≡3(mod4).p\equiv 3\pmod{4}.
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