What is the remainder when $\displaystyle (x+1)^n$ is divided by $\displaystyle (x-1)^4$

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- Jul 16th 2010, 02:02 AMpankajAnother remainder problem
What is the remainder when $\displaystyle (x+1)^n$ is divided by $\displaystyle (x-1)^4$

- Jul 16th 2010, 03:19 AMundefined
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.