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Math Help - MATH question - induction!?

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    MATH question - induction!?

    Let a,b be two positive natural numbers. Prove that for every positive odd number n, a^n + b^n is divided by a+b
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  2. #2
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    Quote Originally Posted by tukilala View Post
    Let a,b be two positive natural numbers. Prove that for every positive odd number n, a^n + b^n is divided by a+b
    Hint: Prove that a^n + b^n = (a+b)\left( \sum_{k=0}^{n-1} (-1)^k a^{k-n} b^k \right)
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  3. #3
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    Quote Originally Posted by ThePerfectHacker View Post
    Hint: Prove that a^n + b^n = (a+b)\left( \sum_{k=0}^{n-1} (-1)^k a^{k-n} b^k \right)
    Here is the expanded notation [n is a positive odd integer]:

    a^n + b^n = (a + b)(a^{n-1} - a^{n-2}b + a^{n-3}b^2 - \cdots + a^2b^{n-3} - ab^{n-2} + b^{n-1})
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