Show for any integer x, gcd(a,b)=gcd(a,b+ax)=gcd(a+bx,b) [NT-Ch.2-S2.4] - Part 7

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For any integer x prove that, gcd(a,b)=gcd(b,a)=gcd(a,-b)=gcd(-a,b)=gcd(a,b+ax) For any integer x prove that, gcd(a,b)=gcd(b,a)=gcd(a,-b)=gcd(-a,b)=gcd(a,b+ax)
BĂ©zout BĂ©zout's identity: ax+by=gcd(a,b)