Me stumped by math!

[Turin39789]

And no, this isn't my homework.


7^381 / 5

What is the remainder.

No calculator, so obviously there is a fraction or exponent trick that I'm not aware of.


ATOT make me smart!

 

[chuckywang]

a^(4*x) = 1 mod 5 by Fermat's Little Theorem. Since, 381 = 1 mod 4 then 7 ^ 381 = 7 ^ 1 = 2 mod 5.

 

[Chronoshock]

When you multiply 7 repeatedly, the one's place will be 7, 9, 3, 1, 7, ...
The remainder when divided by 5 is going to be 2, 4, 3, 1, 2, ...

 

[Turin39789]

so 2?

 

[esun]

Yes. This is modular arithmetic (in case you want to look it up).