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b >= q + s

Source: Polish MO Finals 1969 p4

August 22, 2024
agebrainequalities

Problem Statement

Show that if natural numbers a,b,p,q,r,sa,b, p,q,r,s satisfy the conditions qr−ps=1     and     pq<ab<rs,qr- ps = 1 \,\,\,\,\, and \,\,\,\,\, \frac{p}{q}<\frac{a}{b}<\frac{r}{s}, then b≥q+s.b \ge q+s.
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