4. Suppose x + y = 2, and y is odd. (i). Prove that r is...

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4. Suppose x² + y² = 2², and y is odd. (i). Prove that r is even, so z is odd. (ii). Prove that (iii). Prove that 3m, n such that 2+y 2 Hint: Use (ii) and the result of Problem 3. (vi). Conclude that I m², 2 = (x, y, z) = 1 = 1. 229= z+yz-y 2 2 x = 2mn, y=m²-n², 2=m² + n². 4. Suppose x² + y² = 2², and y is odd. (i). Prove that r is even, so z is odd. (ii). Prove that (iii). Prove that 3m, n such that 2+y 2 Hint: Use (ii) and the result of Problem 3. (vi). Conclude that I m², 2 = (x, y, z) = 1 = 1. 229= z+yz-y 2 2 x = 2mn, y=m²-n², 2=m² + n².

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i Since x2 y2 z2 we have x2 z2 y2 Since y is odd y2 is odd Since the sum of two even numbers is alwa... View the full answer