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Find all integer solutions to y^2=x^3-p^2x, p is a prime

Source: Indian IMO Training Camp 2007-ST 4 P2

March 5, 2011
modular arithmeticDiophantine equationnumber theory proposednumber theory

Problem Statement

Find all integer solutions (x,y)(x,y) of the equation y2=x3−p2x,y^2=x^3-p^2x, where pp is a prime such that p≡3mod  4.p\equiv 3 \mod 4.
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