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k=b^c+a, l=a^b+c, m=c^a+b prime numbers

Source: Greece JBMO TST 2006 p2

June 16, 2019
number theoryprime numbersprimesexponential

Problem Statement

Let a,b,ca,b,c be positive integers such that the numbers k=bc+a,l=ab+c,m=ca+bk=b^c+a, l=a^b+c, m=c^a+b to be prime numbers. Prove that at least two of the numbers k,l,mk,l,m are equal.
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