# Math Help - modular calculation

1. ## modular calculation

can anyone help me with this?

calculate 45^41 mod13

i know i'm probably meant to use fermat's little theorem but i can't see where..

thanks!

2. Originally Posted by MariaJJ
can anyone help me with this?

calculate 45^41 mod13

i know i'm probably meant to use fermat's little theorem but i can't see where..

thanks!

$45\equiv 6\,(mod\,13)\Longrightarrow 45^{41}=6^{41}=\left(6^{13}\right)^3\cdot 6^2=6^3\cdot 6^2=\left(6^2\right)^2\cdot 6=10^2\cdot 6=2\,\,(mod\,\,13)$

Tonio

3. Originally Posted by tonio
$45\equiv 6\,(mod\,13)\Longrightarrow 45^{41}=6^{41}=\left(6^{13}\right)^3\cdot 6^2=6^3\cdot 6^2=\left(6^2\right)^2\cdot 6=10^2\cdot 6=2\,\,(mod\,\,13)$

Tonio
@Tonio-If you can confirm (a yes/no would be sufficient plz)
$
\left(6^{13}\right)^3\cdot 6^2=6^3\cdot 6^2$

This came from Fermat't little thoerm = $a^p \equiv a mod p$
Correct?

4. Originally Posted by aman_cc
@Tonio-If you can confirm (a yes/no would be sufficient plz)
$
\left(6^{13}\right)^3\cdot 6^2=6^3\cdot 6^2$

This came from Fermat't little thoerm = $a^p \equiv a mod p$
Correct?

Yes ssssir!

Tonio