Question

Prove or disprove that the only solutions of

ab = c (mod a+b)
ac = b (mod a+c)
bc = a (mod b+c)

in positive coprime integers a,b,c are {1,1,1} and {5,7,11}

Answer 1

interesting problem
one trivial observation is that \((a,b)=1 \implies (ab,a+b)=1\)