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Is $D(x) + D(y) \leq D(xy)$ true when $\gcd(x, y)=1$ and $xy$ is deficient?

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#elementary-number-theory #inequality #gcd-and-lcm #divisor-sum
640
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gcd of power plus one

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#elementary-number-theory #gcd-and-lcm
301
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Generalization of Division by GCD

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#gcd-and-lcm
608
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Square root of a prime is irrational

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#elementary-number-theory #radicals #gcd-and-lcm #rationality-testing
391
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Prove that for any $m > 0$, $\gcd(mb,mc) = m\gcd(b,c)$.

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#number-theory #gcd-and-lcm #euclidean-algorithm
663
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Proof: there exist $x,y\in \mathbb Z$ such that $xa+yb=\gcd (a,b)$

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#proof-verification #gcd-and-lcm
9.4k
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Let $q=\gcd(x,y)$. Prove that if $x\nmid zq$ then $x \nmid yz$.

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#elementary-number-theory #gcd-and-lcm
884
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Show: $\gcd(a,b)=\gcd(a,c)=1\implies\gcd(a,bc)=1$

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#gcd-and-lcm
69
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$(x,y) \in \mathbb Z \times\mathbb Z$ with $336x+378y=\gcd(336,378)$

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#diophantine-equations #gcd-and-lcm #euclidean-algorithm
1.7k
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find and prove the necessary and sufficient condition in which (a,b)=[a,b]

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#divisibility #gcd-and-lcm #least-common-multiple
94
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if $a\cong b\pmod m$ prove $(a,m)=(b,m)$

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#elementary-number-theory #divisibility #congruences #gcd-and-lcm
351
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Expressing the GCD of 3 polynomials as a linear combination.

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#polynomials #gcd-and-lcm
1.2k
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How to find the GCD of $29-3i$ and $11+10i$

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#abstract-algebra #ring-theory #complex-numbers #gcd-and-lcm #finite-rings
45
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Problem related to divisors

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#integers #gcd-and-lcm
90
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Find greatest common divisor for two given polynomials

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#abstract-algebra #polynomials #gcd-and-lcm

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