1996 IMO Problems/Problem 6

Problem

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 $x_i=x_j$ .

Solution

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1996 IMO (Problems) • Resources
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1996 IMO Problems/Problem 6

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