It is known that a, B and C are all integers. When the value of the algebraic formula 7a + 2B + 3C can be divisible by 13, can the value of the algebraic formula 5A + 7b-22c be divisible by 13? Why?

It is known that a, B and C are all integers. When the value of the algebraic formula 7a + 2B + 3C can be divisible by 13, can the value of the algebraic formula 5A + 7b-22c be divisible by 13? Why?

Let x, y, Z, t be integers, and suppose 5A + 7b-22c = x (7a + 2B + 3C) + 13 (Ya + ZB + TC) (1) compare the coefficients of the above formula A, B, C, there should be 7x + 13y = 52X + 13z = 7 (2) 3x + 13T = - 22, take x = - 3, we can get y = 2, z = 1, t = - 1, then there is 13 (2a + B-C) - 3 (7a + 2B + 3C) = 5A + 7b-22c (3) since 3 (7a + 2B + 3C) and 13 (2a + B-C) can be divisible by 13, 5A + 7b-22c can be divisible by 13