In number theory, there's a simple yet powerful theorem called Bzout's identity, which states that for...

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In number theory, there's a simple yet powerful theorem called Bézout's identity, which states that for any two integers a and b (with a and 6 not both zero) there exist two integers r and s such that ar+bs= ged(a, b). Use Bézout's identity to prove the following statements (you may assume all variables are integers): (a) If dla and d]b, then dl ged(a, b). (b) If al be and ged(a, b) = 1, then alc. In number theory, there's a simple yet powerful theorem called Bézout's identity, which states that for any two integers a and b (with a and 6 not both zero) there exist two integers r and s such that ar+bs= ged(a, b). Use Bézout's identity to prove the following statements (you may assume all variables are integers): (a) If dla and d]b, then dl ged(a, b). (b) If al be and ged(a, b) = 1, then alc.

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