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Math Help - Another remainder problem

  1. #1
    Senior Member pankaj's Avatar
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    Another remainder problem

    What is the remainder when (x+1)^n is divided by (x-1)^4
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  2. #2
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by pankaj View Post
    What is the remainder when (x+1)^n is divided by (x-1)^4
    Not sure if this is what the question designer intended, but I'll assume x > 1, then gcd(x-1, x+1) is either 1 or 2 depending on whether x is even or odd, respectively. If gcd is 1, you can use Euler's theorem to reduce the exponent. If gcd is 2, you can use Chinese remainder theorem along with Euler's theorem to solve by letting (x-1)^4 = 2^m*y where y is odd.
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