Write a proof by contradiction of the following. Let x and y be integers. If x and y satisfy the equation 3x + 5y = 153 then at least one of x and y is odd. Let x and y be integers that satisfy the equation 3x + 5y = 153. Suppose, to the contrary, that both x and y are even. Then x = (3k₁+5k₂) is -Select-- 153 = 3x + 5y = K₂ = . But 153 = 2 for some integer k₂ and y = +1 is also --Select--- for some integer k₂. Then This contradicts Axiom 1.2.

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