1. If there exists integers x and y for which ax+by=gcd(a,b), then gcd(x,y)=1.
2. Given an odd integer a, establish that a^2+(a+2)^2+(a+4)^2+1 is divisible by 2
3. Prove that for a positive integer n and any integer a, gcd(a, a+n) divides n; hence gcd(a, a+1)=1.