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(a + b)(b + c)(c + a)/ abc is integer - All-Russian MO 1996 Regional (R4) 9.3

Source:

September 23, 2024

number theoryInteger

Problem Statement

Let

a, b

and

c

be pairwise relatively prime natural numbers. Find all possible values of

\frac{(a + b)(b + c)(c + a)}{abc}

if known what it is integer.