MathDB
2016 Team #5

Source:

December 30, 2016

Problem Statement

Find all prime numbers pp such that y2=x3+4xy^2 = x^3+4x has exactly pp solutions in integers modulo pp.
In other words, determine all prime numbers pp with the following property: there exist exactly pp ordered pairs of integers (x,y)(x,y) such that x,y∈{0,1,…,p−1}x,y \in \{0,1,\dots,p-1\} and p divides y2−x3−4x. p \text{ divides } y^2 - x^3 - 4x.
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