Prove that $\gcd(2^a-1,2^b-1)=2^{\gcd(a,b)}-1$
Hints-
$1$. Use Euclids Lemma
$2$. $2^a=2^{a\%c}\mod (2^c)-1$
$3$. If $a=q\cdot b+c$ then $2^a=(2^c)^q\cdot 2^r$
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Is this homework? What have you tried? – A.S Feb 08 '13 at 04:36
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1More generalized version: http://math.stackexchange.com/questions/7473/prove-that-gcdan-1-am-1-a-gcdn-m-1 – lab bhattacharjee Feb 08 '13 at 04:44
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@lab, I think the more general question is also answered (just not asked) at the question I cited. – Gerry Myerson Feb 08 '13 at 04:49