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Given two integers $a$ and $b$, determine if $a$ and $b$ are equivalent modulo any $k \, (k: 1 \lt k \lt |a - b|)$.
If $\exists$ an integer $ (k: 1 \lt k \lt |a - b|) \text{ and }a \equiv b \mod k$, then the algorithm would return true, otherwise it would return false.
I thought of this problem today.
Before attempting to solve it, I want to know if there is existing literature on the problem. However, I would need to know the problem to do research on it.
You just need to check if $|a-b|$ is divisible by a some integer $k$. You can reduce it to the integer factorization problem if you are not interested in the trivial divisors 1 and $|a-b|$.
