This is what I read:

One can test if there exist integers x and y such that

$c\cdot x + j = d \cdot y + k$,

if $(k-j)\mod(\gcd(c,d)) = 0$

How can one see that?

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PS: I understand what $\gcd $ and mod operations do.

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PSS: Source: 1st frame of slide 6 within http://www.cs.arizona.edu/~collberg/Teaching/553/2011/Handouts/Handout-33.pdf

`d`

in lhs and in the rhs are not the same.. – beteraba Dec 7 at 13:10