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NUMBER THORY

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March 5, 2017
number theory

Problem Statement

Let a,b,ca,b,c be distinct positive integers and let r,s,tr,s,t be positive integers such that: ab+1=r2,ac+1=s2,bc+1=t2ab+1=r^2,ac+1=s^2,bc+1=t^2 Prove that it is not possible that all three fractionsrts,rst,str \frac{rt}{s}, \frac{rs}{t}, \frac{st}{r} are integers.
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