Discrete Math.

Let x and y be integers. If x and y satisfy the equation. 3x + 5y = 143. then at least one of x and y is odd.

Let x and y be integers that satisfy the equation3x + 5y = 143. Suppose, to the contrary, that both x and y are even. Then x =(2k1) for some integer k1 and y = (2k2) for some integer k2. Then143 = 3x + 5y = ( _____ )k1 +( ____ ) k2 = ______ (3k1 + 5k2)iseven. But143 = 2 ( ____ ) + 1is also odd. This contradicts Axiom 1.2.