Thread: Modulo/congruence proof help

1. If then

2. Every positive integer is congruent to the sum of its digits (mod 9).

1. Use the fact that there exists such that:

You can also show that this is unique. by supposing that there exists more than one unique solution, i.e. and for some and arriving at a contradiction.

2. Here: Congruence

Thanks for the link for the second one! We just had to prove that so I guess I should have been able to figure that one out but I needed a push in the right direction!

For the first one, I'm still unsure. I actually had what you have written on my paper, but I'm still unsure of how the "b" fits into the problem. I have but I need or right? I could divide by x, giving but can I let since that's a fraction?

We know that there exists some such that:

By definition, this is the same as saying:

But since has already been determined, this is the we were looking for !

Oh, duh! Haha for some reason I was thinking I needed to prove . Thanks for all of your help!