Let
be an infinite sequence of strictly positive integers, so that
for any
Prove that there exists an infinity of terms
, which can be written like
with
strictly positive integers and
.
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Let $a_{1}, \ldots, a_{n}$ be an infinite sequence of strictly positive integers, so that $a_{k} < a_{k+1}$ for any $k.$ Prove that there exists an infinity of terms $a_m$, which can be written like $a_m = x \cdot a_p + y \cdot a_q$ with $x,y$ strictly positive integers and $p \neq q$.
Školjka