IMO 1984 LL SWE56

Let a, b, c be nonnegative integers such that a \leqb \leqc, 2b ̸=

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IMO 1984 LL SWE56

Origin: SWE

Problem

Let a, b, c be nonnegative integers such that a \leqb \leqc, 2b ̸= a + c and a+b+c is an integer. Is it possible to find three nonnegative integers d, e, and f such that d \leqe \leqf, f ̸= c, and such that a2+b2+c2 = d2 + e2 + f 2?