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

What these 12 flashcards ask

State Fermat's little theorem.
Alternative form of Fermat's little theorem?
How do you reduce a^k\pmod p?
Least positive residue of 4^{20} modulo 7?
Remainder when 12^{50} is divided by 7?
When does ax\equiv b\pmod n have a solution?
How many solutions modulo n does it have?
What is the multiplicative inverse of a modulo n?
How do you find a multiplicative inverse?
Inverse of 17 modulo 40?
Solve 7x\equiv3\pmod{11}.
Solve a congruence when d=hcf(a,n)1 and d\mid b.

Exam questions on Fermat's little theorem and congruence equations

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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).