• 1.

  draft
  Find gcd g of two positive integers x, y and also find integers a, b such that ax+by=g with prescribed intervals for a and b.
• 2.

  Doesn't work
  Pick four numbers from $1900\dots 2015$ and ask the student to factorise them. Custom marking scripts make sure the student has entered a complete factorisation.
• 3.

  Doesn't work
  Factorising 5 to 7 digit numbers into a product of prime powers. Uses the marking algorithms from question 1 of this CBA
• 4.

  draft
  Given one solution of the quadratic equation in $\mathbb{Z}_n$ where $n=pq$ is a product of two primes find the other 3 solutions.
• 5.

  draft
  Calculations in $\mathbb{Z_n}$ for three values of $n$.     
• 6.

  Ready to use
  Express various integers and rationals mod $\mathbb{Z}_3, \;\mathbb{Z}_5,\;\mathbb{Z}_7,\;\mathbb{Z}_{11}$
• 7.

  Has some problems
  Modular arithmetic
• 8.

  draft
  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.
• 9.

  draft
  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 $\operatorname{gcd}(c_1,n_1)=1,\;\operatorname{gcd}(c_2,n_2)=1,\;\operatorname{gcd}(n_1,n_2)=1$
• 10.

  Doesn't work
  Solving an equation of the form $ax \equiv b\;\textrm{mod}\;n$ where $a$ and $n$ are coprime.
• 11.

  Has some problems
  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.
• 12.

  draft
  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 $\operatorname{gcd}(n_1,n_2,n_3)=1$
• 13.

  Ready to use
  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 $\operatorname{gcd}(n_1,n_2,n_3)=1$
• 14.

  draft
  Number Theory.  Given $n \in \mathbb{N}$ find $\mu(n),\;\tau(n),\;\sigma(n),\;\phi(n).$
• 15.

  draft
  Given $\frac{a}{b} \in \mathbb{Q}$ for suitable choices of $a$ and $b$, find all $n \in \mathbb{N}$ such that $\phi(n)=\frac{a}{b}n$.
• 16.

  draft
  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.
• 17.

  Needs to be tested
  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.
• 18.

  draft
  Given $m \in \mathbb{N}$, find the smallest natural number $n \in \mathbb{N}$ with $\tau(n)=m$ divisors.

There are no questions in this group.