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Polish Algebra

Source: Polish Mathematical Olympiad 2016 P5- Final Round

April 8, 2016
algebrareal numberSum of Squares

Problem Statement

There are given two positive real number a<ba<b. Show that there exist positive integers p, q, r, sp, \ q, \ r, \ s satisfying following conditions: 11. a<pq<rs<ba< \frac{p}{q} < \frac{r}{s} < b. 2.2. p2+q2=r2+s2p^2+q^2=r^2+s^2.
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