Least positive rest in division?

[jdnhldn]

Homework Statement

Find the least positive rest in division of 7^35 with 5

Homework Equations

(7^35)/5

The Attempt at a Solution

7^35=378818692265664781682717625943 => 378818692265664781682717625943/5... Uhhhhh this is not the way I am supposed to take right?

 

[jgens]

What does the phrase "least positive rest" mean? I did a brief google search on it and didn't find anything helpful.

 

[Mark44]

By "least positive rest" I think the OP means "remainder." Presumably properties of modular arithmetic should be used to find this remainder.

For example, 7 $\equiv$ 2 (mod 5), so 7³⁵ $\equiv$ 2³⁵ (mod 5). Does any of this look familiar?

 

[jdnhldn]

What does the phrase "least positive rest" mean? I did a brief google search on it and didn't find anything helpful.

I am sorry that I got you confused by the translation. Yes, as Mark44 mentioned, it means remainder.

By "least positive rest" I think the OP means "remainder." Presumably properties of modular arithmetic should be used to find this remainder.

For example, 7 $\equiv$ 2 (mod 5), so 7³⁵ $\equiv$ 2³⁵ (mod 5). Does any of this look familiar?

This is exactly what I am looking for and it looks familiar :)

But I don't get how 7^35=2^35 (mod 5) Please explain?

 

[Mark44]

I am sorry that I got you confused by the translation. Yes, as Mark44 mentioned, it means remainder.


This is exactly what I am looking for and it looks familiar :)

But I don't get how 7^35=2^35 (mod 5) Please explain?

As I already explained, because 7 (mod 5) $\equiv$ 2 (mod 5), then 7³⁵ (mod 5)$\equiv$ 2³⁵ (mod 5).