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Japan mathematical olympiad finals 2006, problem 2

Source:

March 3, 2006
number theory proposednumber theory

Problem Statement

Determine all integers kk for which there exist infinitely the pairs of integers (a,b,c)(a,b,c) satisfying the following equation. (a2−k)(b2−k)=c2−k. (a^2-k)(b^2-k)=c^2-k.
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