Let $n,m$ be positive integers and $d = \gcd(n,m). $
Prove that $\gcd(x^{n} -1 ,x^{m} -1) = x^{d} -1$.
Is this correct?
Bezout : integers $r,s$: $\quad r(x^{n} -1) + s(x^{m} -1) = rx^{n} +sx^{m} - (r+s) = x^{d} -1$
Asked
Active
Viewed 63 times
2
-
$r, s$ are polynomials with integer/rational coefficients in this context. – Mark Bennet Oct 19 '13 at 12:30
-
Related : http://math.stackexchange.com/questions/262130/how-to-prove-gcdam-bm-an-bn-a-gcdm-n-b-gcdm-n and http://math.stackexchange.com/questions/7473/prove-that-gcdan-1-am-1-a-gcdn-m-1 – lab bhattacharjee Oct 19 '13 at 12:42