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a^2+ab+b^2=c^2+3 prime diophantine

Source: Czech-Polish-Slovak Junior Match 2012, Individual p2 CPSJ

March 11, 2020
Diophantine equationdiophantineprimesnumber theory

Problem Statement

Determine all three primes (a,b,c)(a, b, c) that satisfied the equality a2+ab+b2=c2+3a^2+ab+b^2=c^2+3.
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