1975 IMO Problems/Problem 2
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Problem
Let 
be an infinite increasing sequence of positive integers. Prove that for every 
there are infinitely many 
which can be written in the form![\[a_m = xa_p + ya_q\]](http://latex.artofproblemsolving.com/e/b/9/eb9bb151d31503625e3290d5c42f87bcda8b767e.png)
with 
positive integers and 
.
