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Find three prime numbers given conditions

Source: RMO 2008, Grade 7, Problem 3

April 30, 2008
inequalitiesnumber theoryprime numbers

Problem Statement

Let p,q,r p,q,r be 3 prime numbers such that 5≤p<q<r 5\leq p <q<r. Knowing that 2p^2\minus{}r^2 \geq 49 and 2q^2\minus{}r^2\leq 193, find p,q,r p,q,r.
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