(Number Theory) gcd (a , b) = 1, if and only if ax + by = 1 for some integers x and y

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gcd(a, b) if and only if there exist integers x, y such that 1 = ax+by [NT-Ch.2-S2.4] - Part 4 gcd(a, b) if and only if there exist integers x, y such that 1 = ax+by [NT-Ch.2-S2.4] - Part 4
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Find integers x and y such that gcd (a, b) = a x + b y /gcd (a, b) as linear combinations of a and b Find integers x and y such that gcd (a, b) = a x + b y /gcd (a, b) as linear combinations of a and b
Bézout Bézout's identity: ax+by=gcd(a,b)
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||Lecture#14||GCD(a,b)=1 iff 1=ax+by, where a,b,x,y∈Z||Examples||Prof.Latif Sajid||Number Theory|| ||Lecture#14||GCD(a,b)=1 iff 1=ax+by, where a,b,x,y∈Z||Examples||Prof.Latif Sajid||Number Theory||