Use the Euclidean algorithm to find integers x and y such that 164x+37y=1. State your answer as a list with x first and y second, separated by a comma.
164x + 37y = 1
164 = 4(37) + 16
37 = 2(16) + 5
16 = 3(5) + 1
1 = 16 - 3(5)
1 = 16 - 3 [ 37 - 2(16) ]
1 = 7(16) - 3(37)
1 = 7 [ 164 - 4(37)] - 3(37)
1 = 165 (7) - 37(28) - 37(3)
1 = 164(7) + 37(-31)
So (x, y) = ( 7, -31)