Given that xy' is congruent to x'y mod p, p is prime and that 0<xy', x'y<p then why can we say that xy'= x'y?

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- May 1st 2012, 07:40 AMalexandrabel90congruent
Given that xy' is congruent to x'y mod p, p is prime and that 0<xy', x'y<p then why can we say that xy'= x'y?

- May 1st 2012, 09:00 AMHallsofIvyRe: congruent
"xy' congruent to x'y mod p" means that xy'- x'y is a multiple of p. if both xy' and x'y are positive and less than p, that "multiple" must be 0.