Problem
If $(a,b)=1$ then $(a, b+1)=1$.
Progress
So far I have,
- Let $d = (a,b)$
- Which implies $d\mid a$ and $d\mid b$
- Which implies there exist $x$ and $y$ such that $d\mid (a)(x) + (b)(y)$
- So I want to find an $x$ and $y$ that can make the equation, $ax+by$ into $(a+1)(x)+(ab)(y)$