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Part of 2006 Greece JBMO TST

Problems(1)

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

Source: Greece JBMO TST 2006 p2

6/16/2019
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.
number theoryprime numbersprimesexponential