I have two prime powers $2^n$ and $5^n$ for some arbitrary $n$. Their gcd is $1$ but how do I get their integer linear combination which is $1$ in terms of $n$. In other words what will be the integers $a,b$ as functions of $n$ such that $a2^n+b5^n=1$.
The reason I am unable to apply the Euclidean algorithm is that I don't know $n$ beforehand.
Any help would be greatly appreciated. Thanks