take 2 prime numbers A and B, when you starting taking multiples of A, the remainders of those multiples after division by B will change at every multiple, and within B repetitions, they would have produced all possible remainders, this is quite 'intuitive' if we take an example.

Let us take 11 and 7.

11 x 1 = 7 x 1 + 4

11 x 2 = 7 x 3 + 1

11 x 3 = 7 x 4 + 5

11 x 4 = 7 x 6 + 2

11 x 5 = 7 x 7 + 6

11 x 6 = 7 x 7 + 3

11 x 7 = 7 x 11 + 0

The sequence of remainder is quite interesting: 4,1,5,2,6,3,0.

I guess it is possible to derive an equation for it depending on the 2 numbers but for now let us try to prove that within 7 multiples of 11, all possible remainders are generated.

It is not very hard:

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