MathDB

8

Part of 1973 IMO Longlists

Problems(1)

If S_k and S_(k+1) are integers, then all S_n are integers

Source: IMO LongList 1973 - P8

6/6/2011
Let aa be a non-zero real number. For each integer nn, we define Sn=an+a−nS_n = a^n + a^{-n}. Prove that if for some integer kk, the sums SkS_k and Sk+1S_{k+1} are integers, then the sums SnS_n are integers for all integers nn.
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