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How many numbers from 7, 13, 14, 21, 26, 39 and 91 divide $$(69^{12} − 38^{12})$$?

I am able to get the answer by calculating it.

But is there is any shorter way by which i can solve this?

Thanks in advance.

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    I think that the point of the exercise was to show that you know how to factor $$x^n-y^n\text{ where n is any positive integer greater than }1$$ and $$x^n+y^n\text{ where n is any positive odd integer greater than 1}$$2014-10-26

6 Answers 6