Problem Solving

Maybe a poor example, some questions like this say: (7^243)+(7^22)-5 divided by 7, what is the remainder?

How to solve this kind of problem?


Thanks

I think it's important to look at the terms and how they fit to solve this question.

(7^243)+(7^22)-5 divided by 7 = [ (7^243) + (7^22) - 5 ] / 7

This expression can be broken down further by dividing 7 into each term.

(7^243)/7 + (7^22)/7 - 5/7

The 1/7 term seemlessly goes into the 7^243 and 7^22 term, because 1/7 = 7^(-1), i.e. two numbers with the same base (7) are being multiplied. This means there is no remainder.

The - 5 term isn't so fortunate. 7 is too big to be to divided into 5, so 5 is the remainder.

Wow how embarrassing, thanks for the correction Anurag@Gurome