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Proof that if $\gcd(a,b) = 1$ then $\gcd(a^n, b^m) = 1$

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#number-theory #elementary-number-theory #gcd-and-lcm
1k
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How do I prove Bézout's identity of polynomials in $F[x]$?

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#polynomials #gcd-and-lcm
405
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GCD in multivariate polynomial ring and quotient ring

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#abstract-algebra #gcd-and-lcm #quotient-group #groebner-basis #multivariate-polynomial
54
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GCD and LCM of powers in GCD domains

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#abstract-algebra #gcd-and-lcm #least-common-multiple
342
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How to find GCD of those two complex polynomials?

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#polynomials #gcd-and-lcm #euclidean-algorithm
595
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General formula for the gcd.

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#number-theory #closed-form #gcd-and-lcm #coprime
262
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prove or disprove if $ab\equiv ac \bmod m$ then $b\equiv c \bmod m$

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#discrete-mathematics #modular-arithmetic #gcd-and-lcm
551
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Factor $x^p-y^p$

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#number-theory #elementary-number-theory #factoring #gcd-and-lcm
57
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Why are these two monic complex polynomials coprime?

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#polynomials #gcd-and-lcm
784
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Method for finding the coefficients in Bezout's identity without using extended euclidean algorithm

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#number-theory #elementary-number-theory #gcd-and-lcm #euclidean-algorithm
230
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"Factor" a number into 1-16 products and sum parts

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#gcd-and-lcm
81
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How to solve $y^3=x(x+1)$ where $x$ and $y$ are integers?

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#elementary-number-theory #divisibility #diophantine-equations #gcd-and-lcm
62
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What is the significance of $(n,m)=1$ in this proof that the Euler phi function is multiplicative?

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#number-theory #proof-explanation #gcd-and-lcm #totient-function
580
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Proof explanation: suppose $a\mid bc$ and $\gcd(a, b) = 1$. Then $a\mid c$.

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#elementary-number-theory #proof-explanation #divisibility #gcd-and-lcm
698
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Compute $\gcd(a+b, 2a+3b)$ if $\gcd(a,b) = 1$

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#elementary-number-theory #divisibility #gcd-and-lcm

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