1. ## coprime question!

some how using the fact that integers a and b are coprime if, and only if, there exist
integers m and n such that $am + bn = 1$ i am trying to find:

m and n to show that

(i) 41 and 68 are coprime, (ii) 71 and 118 are coprime.

i also have to prove:

$3k + 2$ and $5k + 3$ are coprime for all $k\in \mathbb{Z}$

p.s. if anyone knows how you do those symbols for integers, real numbers and rational numbers on latex that would be useful!

thanks

2. $$\mathbb{X}$$ gives $\mathbb{X}$.
You can replace the X with whatever.