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Use Bézout's algorithm to solve $as + bt = \gcd(a,b)$ ,
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Given two numbers, find the gcd, then use Bézout's algorithm to find $s$ and $t$ such that $as+bt=\operatorname{gcd}(a,b)$ .
Greatest common divisor and Bézout's algorithm
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Question in Christian's workspace by Christian Lawson-Perfect

Given two numbers, find the gcd, then use Bézout's algorithm to find $s$ and $t$ such that $as+bt=\operatorname{gcd}(a,b)$ . Finally, find all solutions of an equation $\mod b$ .
Solve a pair of congruences
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solving two simultaneous congruences:

$\begin{eqnarray*} c_1x\;&\equiv&\;b_1\;&\mod&\;n_1\\ c_2x\;&\equiv&\;b_2\;&\mod&\;n_2\\ \end{eqnarray*}$ where $\operatorname{gcd}(c_1,n_1)=1,\;\operatorname{gcd}(c_2,n_2)=1,\;\operatorname{gcd}(n_1,n_2)=1$
Solve congruence in given range
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solving an equation of the form $ax \equiv\;b\;\textrm{mod}\;n$ where $\operatorname{gcd}(a,n)|r$ . In this case we can find all solutions. The user is asked for the two greatest.
Solve three congruences using Chinese Remainder Theorem
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solving three simultaneous congruences using the Chinese Remainder Theorem:

$\begin{eqnarray*} x\;&\equiv&\;b_1\;&\mod&\;n_1\\ x\;&\equiv&\;b_2\;&\mod&\;n_2\\x\;&\equiv&\;b_3\;&\mod&\;n_3 \end{eqnarray*}$ where $\operatorname{gcd}(n_1,n_2,n_3)=1$
Solve three congruences with the Chinese Remainder Theorem
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solving three simultaneous congruences using the Chinese Remainder Theorem:

$\begin{eqnarray*} x\;&\equiv&\;b_1\;&\mod&\;n_1\\ x\;&\equiv&\;b_2\;&\mod&\;n_2\\x\;&\equiv&\;b_3\;&\mod&\;n_3 \end{eqnarray*}$ where $\operatorname{gcd}(n_1,n_2,n_3)=1$
Divide two elements of $\mathbb{Z}[i]$
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

In the Gaussian integer ring $\mathbb{Z}[i]$ , find the remainder $r=r_1+r_2i$ , where $a \gt 0,\;b \gt 0$ , on dividing $a+bi$ by $c+di$ .
Factorise polynomial into irreducible factors
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

$f(X)$ and $g(X)$ are polynomials over $\mathbb{Z}_n$ .

Find their greatest common divisor (GCD) and enter it as a monic polynomial.

Hence factorize $f(X)$ into irreducible factors.
Find greatest common divisor of two polynomials over the rationals
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

$f(X)$ and $g(X)$ as polynomials over the rational numbers $\mathbb{Q}$ .

Find their greatest common divisor (GCD) and enter as a normalized polynomial.

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