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Found problems: 1

1994 Irish Math Olympiad, 1
Tags: quadratics , calculus , integration , algebra , number theory proposed , number theory , Ireland
Let $ x,y$ be positive integers with $ y>3$ and $ x^2\plus{}y^4\equal{}2((x\minus{}6)^2\plus{}(y\plus{}1)^2).$ Prove that: $ x^2\plus{}y^4\equal{}1994.$