Question

For any integer a, gcd(11a + 5,2a + 1) = 1
prove

Answer 1

Suppose it equals x, which isn't 1. Find a contradiction.

Answer 2

again?
oh it was as different person last time
multiply the second by 5, subtract from first

Answer 3

in other words if gcd(a,b) = d, then d divides any linear combination of a and b

Answer 4

so if gcd(11a+5, 2a+1)=d, then d divides
(11a+5)-5(2a+1) and so d divides 1

Answer 5

so that proves it for every integer?