Problem 3

Part of 2020 Brazil Undergrad MO

Problems(1)

Find all matrix in $\mathbb{F}_{13}$

Source: Brazil Undergrad MO 2021

\mathbb{F}_{13} = {\overline{0}, \overline{1}, \cdots, \overline{12}}

be the finite field with

13

elements (with sum and product modulus

13

). Find how many matrix

A

5

5

with entries in

\mathbb{F}_{13}

exist such that

A^5 = I

I

is the identity matrix of order

5

linear algebramatrixBrazilian Undergrad MOBrazilian Undergrad MO 2020number theory