# GCD inequality over numbers with the same set of prime factors

Suppose $m,n\in\mathbb{Z}^+$ have the same set of prime factors.

Does it follow that $\gcd(m+1,n-1)\leq\gcd(m-1,n-1)+2$?

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$m=24$, $n=36$, $\gcd(25,35)=5$, $\gcd(23,35)=1$.