Let x and y be integers satisfying 41x + 53y = 18. Find the residue of x modulo 53.
(Express your answer as an integer from 0 to 52.)
41x + 53y = 18
x = 25, y = - 19
25 mod 53 = 25
Note: There are an infinite number of solutions for x and y. They should have specified the pair, such as: the "smallest pair", which is what I used. There is also a solution where x =- 28 and y = 22, in which case:
-28 mod 53 = - 28
53 + (-28) ==25. In either case , the answer appears to be 25.
