# Another remainder problem

• Jul 16th 2010, 02:02 AM
pankaj
Another remainder problem
What is the remainder when $(x+1)^n$ is divided by $(x-1)^4$
• Jul 16th 2010, 03:19 AM
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Quote:

Originally Posted by pankaj
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.