Fermat's little theorem and congruence equationsEdexcel A-Level Further Maths: Mind map

Exam questions on Fermat's little theorem and congruence equations

1. Work modulo $7$, which is prime.
   Find the remainder when $12^{50}$ is divided by $7$.2 marks
2. Linear congruences of the form $ax\equiv b\pmod n$ are to be solved for integers $x$.
   Solve $7x\equiv3\pmod{11}$.2 marks
3. Consider the numbers $17$ and $40$.
   Use the Euclidean algorithm to show that $17$ and $40$ are coprime.3 marks