Activity for Thursday 13 October

Fermat's Little Theorem: for any prime number p, and any natural number a which is not divisible by p,
$a^{p-1} \equiv 1$ (mod p)


For example, $4^{10} \equiv 1$ (mod 11)
because 11 is a prime number and 4 is not divisible by 11.


Based on your viewing of the video, assigned last time, from Maths by Jay, which discussed Fermat's Little Theorem and how it can be used to simplify some calculations:

Use the above-mentioned fact to find the value of
$4^{1357}$ (mod 11)
















Hint: You'll use the division algorithm on the exponent 1357







You want to rewrite $4^{1357}$ as a power of $4^{10}$, times another power of 4