IMO Shortlist 1984 problem 16

Let $a,b,c,d$ be odd integers such that $0<a<b<c<d$ and $ad=bc$ . Prove that if $a+d=2^k$ and $b+c=2^m$ for some integers $k$ and $m$ , then $a=1$ .

Source: Međunarodna matematička olimpijada, shortlist 1984

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