How Can I solve this problem ! https://cses.fi/problemset/task/1712 Will be grateful if anyone can help. Thank You.

https://codeforces.com/problemset/problem/1110/C IN this problem,when a=2x−1. This implies gcd(a⊕b,a&b)=gcd(2x−1−b,b)=gcd(2x−1,b), since gcd(x,x+y)=gcd(x,y) (for all x and y), hence it's sufficient to find the largest non trivial divisor of a — it will be the desired answer.(From editorial) But,why this work? Can someone please explain the solution in more detail? Will be grateful if anyone can help. /*sorry for poor English*/

How Can I solve this problem!https://www.codechef.com/problems/COZIE Can anyone explain,please?

How Can I solve this problem ! https://vjudge.net/problem/UVA-11904 Will be grateful if anyone can help. Thank You.