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Why isn't $\gcd(x^2+3x+2,x^2+x)=(x+1)$? [unit normalization of gcds]

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#abstract-algebra #euclidean-algorithm
1.3k
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Let $\theta$ be a root of $p(x)=x^3+9x+6$, find the inverse of $1+\theta$ in $\mathbb{Q(\theta)}$

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#abstract-algebra #polynomials #ring-theory #gcd-and-lcm #euclidean-algorithm
97
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Extended GCD of two zero polynomials over finite field

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#polynomials #finite-fields #gcd-and-lcm #euclidean-algorithm
272
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Polynomial division problem- find the degree of the remainder

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#algebra-precalculus #polynomials #euclidean-algorithm
99
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Find a specific solution to a linear Diophantine equation

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#elementary-number-theory #euclidean-algorithm #linear-diophantine-equations
1.4k
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Number of steps of Euclidean algorithm. why $r_i{_+}_2 < \frac{1}{2}r_i$?

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#number-theory #elementary-number-theory #euclidean-algorithm
1.5k
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Computational Complexity of Euclidean Algorithm for Polynomials

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#computational-complexity #euclidean-algorithm
100
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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
540
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Finding alternative solutions to Bezout's Identity

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#number-theory #euclidean-algorithm
46
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How to solve this equation for d

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#modular-arithmetic #euclidean-algorithm
135
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How to solve the equation $15x- 16y= 10$

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#algebra-precalculus #euclidean-algorithm
62
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Is there a "symmetric" way to use the Euclidean algorthm on $R[x,y]$ for a domain $R$?

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#abstract-algebra #polynomials #euclidean-algorithm #euclidean-domain
194
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Predicting the change in the denominator of a continued fraction when reversing the order of $a_1$ through $a_n$.

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#continued-fractions #euclidean-algorithm
87
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Representation of an integer / Euclidean algorithm

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#summation #integers #euclidean-algorithm
170
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Linear combination using extended GCD

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#gcd-and-lcm #binary #euclidean-algorithm

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