Is it okay to prove this by contradiction?

Question

I am learning how to prove and I would like to know whether it is right to prove by this method or if it could prove in any better way.

There is no pair of integers $ a $ and $ b $ for which $ 14a + 2014b = 1$

Assume that the pair exists and from there find the contradiction.

Thanks.

Answer 1

Hint: $14a+2014b=2(7a+1007b)$ Can you go from here?

Answer 2

Not sure if it's perfectly correct but here's what I think

a=(1-2014b)/14 Now as a is an integer so is the b, (1-2014b) should be divisible by 14 i.e. Div. By 2 as well. But as 2014b is even (1-2014b) can never be div. By 2 as it's odd. And hence no soln exist , you can also check other way around. hope it helps pardon otherwise