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Are these gcd proofs valid?

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#elementary-number-theory #solution-verification #gcd-and-lcm
132
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How can I find $\gcd(n^a-1,m^a-1)$?

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#number-theory #elementary-number-theory #gcd-and-lcm
297
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Find $G\left(10^{11}\right)$

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#number-theory #summation #gcd-and-lcm
884
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Solve the equation $x^4+x^3-9x^2+11x-4=0$ which has multiple roots.

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#calculus #polynomials #roots #gcd-and-lcm
126
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Calculating Bezout coefficients and gcd for two numbers that divide evenly with no remainder.

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#number-theory #gcd-and-lcm
1.2k
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Let $D$ be a PID and $a$ and $b$ be nonzero elements of $D$. Prove that there exist elements $s$ and $t$ in $D$ such that $\gcd(a, b) = as + bt$.

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#abstract-algebra #ring-theory #gcd-and-lcm #principal-ideal-domains
174
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If $x$ and $y$ are solitary numbers satisfying $\gcd(x,y)=1$, under what conditions does it follow that $xy$ is also solitary?

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#elementary-number-theory #gcd-and-lcm #conjectures #divisor-sum #arithmetic-functions
38
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Finding a greatest common divisor

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#gcd-and-lcm
104
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Find $\gcd(3^{20} + 3, 3^{21} +6)$

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#gcd-and-lcm
89
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How can I calulate $\gcd(ab,c)$?

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#number-theory #gcd-and-lcm
98
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Bezout's identity on $F[x]$ with constraints

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#abstract-algebra #polynomials #ring-theory #gcd-and-lcm #euclidean-algorithm
55
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Prove that the there exists a single Reduced residue system.

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#number-theory #gcd-and-lcm #reduced-residue-system
115
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Prove if $n\mid ab$, then $n\mid [\gcd(a,n) \times \gcd(b,n)]$

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#elementary-number-theory #divisibility #gcd-and-lcm
1.7k
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Greatest Common Divisor in a ring definition

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#abstract-algebra #gcd-and-lcm
187
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Proof verification: If $gcd(n,9)=3$ then $gcd(n^2,9)=9$, $p∣n \implies p∣n^2$, $p∣n^2\implies p∣n$.

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#number-theory #proof-verification #divisibility #gcd-and-lcm

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