(A+xB)/C = y

An algorithm to find x, when A, B, C and y are integers.


Is there an already is such an algorithm out there, to generically and efficiently find a place where an integer summation series such as A+B+B+B+... becomes exactly divisible by some other integer C.

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I think, [notexactly] from Halfbakery has a point:

"Unless I'm misunderstanding the problem statement, this seems like a trivial variant of the least common multiple problem, which can be solved by several algorithms [link]. (A+xB)/C = y seems to me to be equivalent to y = LCM(A - C, B)."

Perhaps the solution is simple, but I had not yet verified this (TBD later).