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Necessary condition of Diophantine equation to have integer solution?

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#abstract-algebra #divisibility #gcd-and-lcm
518
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The sum of two positive integers is $2310$ and $11$ is their g.c.d. How many pairs of such numbers are possible?

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#elementary-number-theory #gcd-and-lcm
107
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If $\gcd(a,b)=1$ then $\gcd(a^2-b^2,a^2+b^2)=1$

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#elementary-number-theory #gcd-and-lcm
41
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Prove that $(m,n) = (s,n) = 1$ if and only if $(ms,n)=1$

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#divisibility #integers #gcd-and-lcm #coprime
432
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Find out if polynomial has inverse in quotient ring

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#abstract-algebra #polynomials #ring-theory #gcd-and-lcm
370
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$\operatorname{lcm}(a,b)=ab$ if and only if $\gcd(a,b)=1$

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#abstract-algebra #gcd-and-lcm #least-common-multiple
4.1k
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If $\gcd(a,b)=1$, then $\operatorname{lcm}(a,b)=ab$

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#elementary-number-theory #proof-verification #gcd-and-lcm #least-common-multiple
424
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Is it true that $\gcd(a,b)$ = $\gcd(a,bk)$ for some integer k?

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#gcd-and-lcm
348
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Is it possible to simplify this expression even further?

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#elementary-number-theory #gcd-and-lcm #divisor-sum #arithmetic-functions #perfect-numbers
166
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Doubt in proof of Proposition 4.5 from Patrick Morandi's *Field and Galois Theory*

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#abstract-algebra #polynomials #field-theory #gcd-and-lcm #splitting-field
137
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Greatest common divisor property: $\gcd(a, b)=\gcd(a+nb, b)$

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#elementary-number-theory #gcd-and-lcm
59
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Is this method to calculate gcd of two polynomials correct?

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#polynomials #gcd-and-lcm
63
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how to compute $\gcd(\frac{a}{b},\frac{c}{d})$?

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#number-theory #gcd-and-lcm #least-common-multiple
51
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Greatest common divisors of a family of polynomials

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#abstract-algebra #number-theory #polynomials #gcd-and-lcm
113
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Doubt regarding the manipulation of Bézout's identity

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#number-theory #gcd-and-lcm #euclidean-algorithm

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