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Number of subsets of size $k$ with a given GCD

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#elementary-number-theory #gcd-and-lcm #mobius-function #mobius-inversion
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Why does the Euclidean algorithm for finding GCD work?

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#gcd-and-lcm #euclidean-algorithm
92
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Prob. 15, Sec. 1.3, in Herstein's TOPICS IN ALGEBRA 2nd ed: If $(m, n)=1$, then, given $a$ and $b$, there is an $x$ such that

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#elementary-number-theory #proof-verification #modular-arithmetic #gcd-and-lcm
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Is the equality $(x+y) \cdot lcm(x,y) = y \cdot lcm(x,x+y)$ true?

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#number-theory #gcd-and-lcm
409
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Two integers whose product is square

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#number-theory #elementary-number-theory #gcd-and-lcm #square-numbers
30
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no unique solution - linear equation

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#number-theory #elementary-number-theory #gcd-and-lcm
337
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The identity element of $(\mathbb{N} , \gcd)$.

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#abstract-algebra #gcd-and-lcm #semigroups #monoid
366
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multiplicative function - gcd - lcm

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#number-theory #elementary-number-theory #gcd-and-lcm #multiplicative-function
99
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identity element of $(D_n ,\gcd)$

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#abstract-algebra #gcd-and-lcm #monoid
61
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Find $f \in \mathbb{Q}(X)$ so that the ideal $(2,X)f = (2f,Xf) \subset \mathbb{Z}[X]$

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#ring-theory #gcd-and-lcm
1.6k
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If $x|yz$ and $\gcd(x, y)$ = 1 then $x|z, x, y, z \in \mathbb{Z}$

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#gcd-and-lcm
529
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Greatest prime divisor of $ n^2+1$

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#number-theory #prime-numbers #divisibility #gcd-and-lcm
158
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Given d = gcd(c,n), why there exists relatively prime integers r and s, such that c = rd and n = sd

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#elementary-number-theory #gcd-and-lcm #coprime
481
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Given $\gcd (a,b,c)=12$, find $\gcd (a,b ,c,16)$

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#elementary-number-theory #gcd-and-lcm
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find $\gcd(2n+1,n)$ assuming that $n$ is non negative integer

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#gcd-and-lcm

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