IMO 1979 LL FRA23

Consider the set E consisting of pairs of integers (a, b), with a \geq

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IMO 1979 LL FRA23

Origin: FRA

Problem

Consider the set E consisting of pairs of integers (a, b), with a \geq 1 and b \geq1, that satisfy in the decimal system the following properties: (i) b is written with three digits, as \alpha2\alpha1\alpha0, \alpha2 ̸= 0; (ii) a is written as \betap . . . \beta1\beta0 for some p; (iii) (a + b)2 is written as \betap . . . \beta1\beta0\alpha2\alpha1\alpha0. Find the elements of E.