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On the equation y^2 ≡ x^3 - x (mod p)

Source: Turkey National Olympiad 2002 - D2 - P1

March 11, 2011
modular arithmeticquadraticsnumber theoryprime numbersnumber theory unsolved

Problem Statement

Find all prime numbers pp for which the number of ordered pairs of integers (x,y)(x, y) with 0≤x,y<p0\leq x, y < p satisfying the condition y^2 \equiv  x^3 - x \pmod p is exactly p.p.
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