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$Old$ May 6th, 2008, 06:49 PM

mandy123 $mandy123 is offline$

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$Unhappy$ prove tha if k/n

Prove that if k and n are positive integers with n>k>1 such that k divides n, then ((2^k)-1) divides ((2^n)-1)

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$Old$ May 6th, 2008, 07:21 PM

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Originally Posted by mandy123 $View Post$

Prove that if k and n are positive integers with n>k>1 such that k divides n, then ((2^k)-1) divides ((2^n)-1)

In general if $k|n$ then $a^k-1$ divides $a^n-1$ .
This is because $n=km$ thus $a^{km}-1 = (a^k)^m - 1$ .
Now use identity for factoring $x^n - y^n$ .

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