1. ## Modular Mathematics

Hi there,
This is an extension of a previous post and i was hoping someone could check my answer.

I have to calculate $\displaystyle 17^{4250} \ mod \ 190$

Here is my solution:

$\displaystyle \varphi (190) = 72$

Then by Euler's Theorem
$\displaystyle 17^{72} \equiv \ 1 (mod \ 190)$ since gcd(17,190) = 1

Now
4250 = 72 * 59 + 2

So
$\displaystyle 17^{4250} \equiv \ (17^{72})^{59} * 17^{2} \ \equiv \ 1^{59} * 17^{2} \ \equiv \ 99 (mod \ 190)$

is that correct?

Thanks

2. Originally Posted by Maccaman
Hi there,
This is an extension of a previous post and i was hoping someone could check my answer.

I have to calculate $\displaystyle 17^{4250} \ mod \ 190$

Here is my solution:

$\displaystyle \varphi (190) = 72$

Then by Euler's Theorem
$\displaystyle 17^{72} \equiv \ 1 (mod \ 190)$ since gcd(17,190) = 1

Now
4250 = 72 * 59 + 2

So
$\displaystyle 17^{4250} \equiv \ (17^{72})^{59} * 17^{2} \ \equiv \ 1^{59} * 17^{2} \ \equiv \ 99 (mod \ 190)$

is that correct?

Thanks

I agree