IMO 1979 LL POL52

Let a real number \lambda > 1 be given and a sequence (nk) of positive

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IMO 1979 LL POL52

Origin: POL

Problem

Let a real number \lambda > 1 be given and a sequence (nk) of positive integers such that nk+1 nk

\lambda for k = 1, 2, . . . . Prove that there exists a positive integer c such that no positive integer n can be represented in more than c ways in the form n = nk + nj or n = nr −ns.