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Math olympiad problem
kathleencarrll
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Let a and b be positive whole integers, for which a^2 - b^2 is a power of two. Prove that a^2 + b^2 is the sum of two powers of two (powers of two are 2^0, 2^1, 2^2 …
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kathleencarrll
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hint: what can a+b and a-b be?
JFCautainEU
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a² - b² = (a+b)(a-b). Since a and b are integers, those two terms are also powers of two. (a-b)² + (a+b)² = 2a²+2b² is a sum of two powers of 2
ADeshchytsia
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