# Modular Mathematics

• Mar 28th 2009, 09:14 PM
Maccaman
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 $17^{4250} \ mod \ 190$

Here is my solution:

$\varphi (190) = 72$

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

Now
4250 = 72 * 59 + 2

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

is that correct?

Thanks :)
• Mar 28th 2009, 09:20 PM
TheEmptySet
Quote:

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 $17^{4250} \ mod \ 190$

Here is my solution:

$\varphi (190) = 72$

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

Now
4250 = 72 * 59 + 2

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

is that correct?

Thanks :)

I agree (Clapping)