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Remainders of Euclid's algorithm

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#euclidean-algorithm
202
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How can I use the relationship between the Fibonacci numbers and the EA to fill squares?

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#algebra-precalculus #fibonacci-numbers #euclidean-algorithm
1.7k
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GCD Euclid's algorithm as solution to the 2-buckets water puzzle

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#puzzle #gcd-and-lcm #euclidean-algorithm
65
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Find all pairs of positive integers $(x, y)$ for which $261x + 48y = 7881$

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#number-theory #cryptography #euclidean-algorithm
95
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What can be said about the prime decomposition of the Bezout coefficients $\beta(a,b)$?

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#number-theory #elementary-number-theory #prime-factorization #euclidean-algorithm
1k
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Help proving polynomials division algorithm in $R[x]$ where $R$ is a domain.

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#abstract-algebra #polynomials #ring-theory #field-theory #euclidean-algorithm
1.6k
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How does the (extended) Euclidean algorithm generalize to polynomials?

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#elementary-number-theory #polynomials #euclidean-algorithm
144
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Found $x^8$ while calculating inverse of $(x^6+1)$ in finite field $GF(2^8)$. Help???

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#finite-fields #extension-field #euclidean-algorithm
88
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how to work out a computer program running time

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#abstract-algebra #algorithms #recursive-algorithms #euclidean-algorithm #python
972
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How does the Euclidean Algorithm apply on exponents m and n to show that $gcd(p^m-1, p^n-1) = p^{gcd(m,n)}-1$

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#elementary-number-theory #gcd-and-lcm #euclidean-algorithm
243
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Solving nonlinear Diophantine equations with Euclid's Lemma

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#number-theory #elementary-number-theory #diophantine-equations #euclidean-algorithm
148
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How to calculate $\varphi(103)$?

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#elementary-number-theory #totient-function #euclidean-algorithm
22
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linear equation with floating constants

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#euclidean-algorithm
49
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How to prove that if $(ab,n)=1$ then, $(r,n)=1$?

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#elementary-number-theory #divisibility #gcd-and-lcm #euclidean-algorithm
168
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Prove that $\gcd(P, P')$ is an irreducible polynomial over $\Bbb R.$

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#linear-algebra #derivatives #polynomials #euclidean-algorithm

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