I encountered the claim that modulo is globally mathematically defined as $$a \bmod b = a - b \left\lfloor\frac{a}{b}\right\rfloor\;.$$ I asked for a source and the claimant could/did not provide one.
On top of how different programming languages handle negative numbers in the divisor or the dividend differently, suggesting that perhaps the mathematical definition is not so unambiguous, it appears that there are also weirdnesses about handling fractions, such that not all definitions will work.
Can someone please help clear this up, taking care to address the supposed mathematical/historical/universal definition of modulo (I'm not really asking about the computer definition as one can just accept each programming language's implementation)?
And, is it possible to provide a citation of some kind?