# Least positive rest in division?

1. Sep 11, 2010

### jdnhldn

1. The problem statement, all variables and given/known data

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

2. Relevant equations

(7^35)/5

3. The attempt at a solution

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

2. Sep 11, 2010

### jgens

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

3. Sep 11, 2010

### Staff: Mentor

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?

4. Sep 12, 2010

### jdnhldn

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?

5. Sep 12, 2010

### Staff: Mentor

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