Modular arithmetic and divisibility testsEdexcel A-Level Further Maths: Mind map

Exam questions on Modular arithmetic and divisibility tests

1. The integers $a$ and $b$ satisfy $a\equiv4\pmod9$ and $b\equiv7\pmod9$.
   Find the least positive residue of $a^2-3b$ modulo $9$.2 marks
2. The six-digit number $N=372\,416$.
   Use a divisibility test to show that $N$ is divisible by $11$.2 marks
3. Work modulo $11$.
   Show that $3^5\equiv1\pmod{11}$.3 marks