Prove or disprove the following: If a,b are nonzero integers with gcd(a,b) = d, then there exist integers m and n such that am+bn=d.

Asked Mar 05 '17 at 00:05

Active Mar 05 '17 at 00:22

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So I tried a bunch of values for a and b and got integers m and n to exist so I believe this conjecture to be true. Can someone please help me formulate a proof.

edited Mar 05 '17 at 00:22

Bill Dubuque

282,220

asked Mar 05 '17 at 00:05

AP123

Look up Bezout's identity – Bram28 Mar 05 '17 at 00:10
That is true. This result is known as Bezout's Theorem. Google for it and you will see many proofs – Juniven Acapulco Mar 05 '17 at 00:10

Prove or disprove the following: If a,b are nonzero integers with gcd(a,b) = d, then there exist integers m and n such that am+bn=d.

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