00:01
Can we want to solve this congruence? so i'm going to rewrite it like this.
00:05
What this means is that 5x minus 4 is congruent to 0 mod 3, which means that 5x minus 4 is 3 times sum number y.
00:26
Okay? so we have to solve the equation.
00:41
Okay, so the way we solve this is like this.
00:44
We know that the gcd of 3 and 5 is equal to 1.
00:51
So the way we would solve this would be to find solutions for 5x minus 3y equals 1, then we can just multiply those solutions by 4 to get solutions to this one up here.
01:11
So to solve this, here's what we do.
01:16
We're going to use the euclidean algorithm.
01:21
So first we divide like this, the back subsub.
02:12
So there's our solution.
02:14
Because we only want one.
02:15
We don't, not looking for all of them or anything like that.
02:19
So x does the job, x equals eight.
02:24
Because if we take our original equation, five times eight is four mod three...