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Prime numbers
Has some problems
Question in Transition to university by Chris Graham

Sort a list of numbers into "prime" or "composite".
Fractions: Lowest form
Draft
Question in Bill's workspace by Bill Foster

Reducing fractions to their lowest form by cancelling common factors in the numerator and denominator. There are 4 questions.
Solve a pair of congruences
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solving a pair of congruences of the form $\begin{align}x &\equiv b_1\;\textrm{mod} \;n_1\\x &\equiv b_2\;\textrm{mod}\;n_2 \end{align}$ where $n_1,\;n_2$ are coprime.
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
Draft
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
Ready to use
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 $\operatorname{gcd}(n_1,n_2,n_3)=1$
Find $\mu(n)$ , $\sigma(n)$ , $\tau(n)$ , $\phi(n)$
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Number Theory.

Given $n \in \mathbb{N}$ find $\mu(n),\;\tau(n),\;\sigma(n),\;\phi(n).$
Find all numbers with given value of $\phi(n)$
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Given $\frac{a}{b} \in \mathbb{Q}$ for suitable choices of $a$ and $b$ , find all $n \in \mathbb{N}$ such that $\phi(n)=\frac{a}{b}n$ .
Find n such that $\phi(n)$ is the given value
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Given $m \in \mathbb{N}$ , find all $n \in \mathbb{N}$ such that $\phi(n)=m$ and enter the largest and second largest if they exist.
Factorise numbers into products of prime powers
Doesn't work
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Factorising 5 to 7 digit numbers into a product of prime powers.

Uses the marking algorithms from question 1 of this CBA
Find n such that $\sigma(n)$ is the given number
Needs to be tested
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

Given $m \in \mathbb{N}$ , find values of $n\in \mathbb{N}$ such that $\sigma(n)=m$ .

There are at most two such solutions in this question.
Finding the highest common factor of two numbers
Ready to use
Question in Transition to university by Lauren Richards

This question tests the student's ability to identify the factors of some composite numbers and the highest common factors of two numbers.

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