1996 IMO Problems/Problem 6


Let $p, q, n$ be three positive integers with $p+q<n$. Let $(x_0,x_1,\cdots ,x_n)$ be an $(n+1)$-tuple of integers satisfying the following conditions:

(i) $x_0=x_n=0$;

(ii) For each $i$ with $1 \le i \le n$, either $x_i-x_{i-1}=p$ or $x_i-x_{i-1}=-q$.

Show that there exists indices $i<j$ with $(i,j) \ne (0,n)$, such that $x_i=x_j$.


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See Also

1996 IMO (Problems) • Resources
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Problem 5
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