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# Positive integers

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If a, b, and c are positive integers satisfying ab + c = bc + a = 13  and ac + b = 41, what is the value of a + b + c?

Nov 16, 2021

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Hello Guest,

If a, b, and c are positive integers satisfying ab + c = bc + a = 13  and ac + b = 41, what is the value of a + b + c?

There are 2 solutions for $$a , b , c \in \mathbb{Z}$$ , namely:

S1: a = 5 ; b = 1 ; c = 8 and

S2: a = 8 ; b = 1 ; c = 5 .

The value (a + b + c) for S1 and btw. S2 is (5 + 1 + 8 =) 14.