MathDB

identity

Source: Ireland 1994

June 29, 2009

quadraticscalculusintegrationalgebranumber theory proposednumber theoryIreland

Problem Statement

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.