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geometric sequence

Source: China south east mathematical Olympiad 2007 problem 7

July 12, 2013
rationumber theoryprime numbersnumber theory unsolved

Problem Statement

Find all triples (a,b,c)(a,b,c) satisfying the following conditions: (i) a,b,ca,b,c are prime numbers, where a<b<c<100a<b<c<100. (ii) a+1,b+1,c+1a+1,b+1,c+1 form a geometric sequence.