Thursday, 1 January 2026

Exercise (4.1).15

Explain why $1055^{210} \not \equiv 1 \pmod {211}$.

The number 211 is prime.


We note that $1055 = 5 \times 211$. This means 211 is a factor of $1055^{210}$, and so 

$1055^{210} \equiv 0 \pmod {211}$

This is why  $1055^{210} \not \equiv 1 \pmod {211}$.