I am reading Naoki Sato's notes on Number Theory: http://donut.math.toronto.edu/~naoki/nt.pdf I am on page 2, and doing Example 1.1... "Let x and y be integers. Prove that 2x+3y is divisible by 17 iff 9x+5y is divisible by 17." There's ALREADY A SOLUTION on the book, but I do not understand it. I've read the theorems and also the other examples and found that I can understand them. I guess this one is different. Can somebody please explain it to me clearer...?? Thanks.