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a prime number in form of 2x^2+3y^2.

Source: Iran 3rd round 2013 - Number Theory Exam - Problem 3

September 11, 2013
modular arithmeticnumber theory proposednumber theory

Problem Statement

Let p>3p>3 a prime number. Prove that there exist x,y∈Zx,y \in \mathbb Z such that p=2x2+3y2p = 2x^2 + 3y^2 if and only if p≡5,11  (mod  24)p \equiv 5, 11 \; (\mod 24) (20 points)
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