B) State and prove Euclidean theorem.

1.	B) State and prove Euclidean theorem.
Answer» Explanation: Proof. The Euclidean Algorithm PROCEEDS by finding a sequence of REMAINDERS, r1, R2, R3, and so on, until one of them is the gcd. We prove by INDUCTION that each ri is a linear combination of a and b. ... The repeated step in the Euclidean Algorithm defines rn+2 so that rn=qrn+1+rn+2, or rn+2=rn−qrn+1.

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Explanation:

Proof. The Euclidean Algorithm PROCEEDS by finding a sequence of REMAINDERS, r1, R2, R3, and so on, until one of them is the gcd. We prove by INDUCTION that each ri is a linear combination of a and b. ... The repeated step in the Euclidean Algorithm defines rn+2 so that rn=qrn+1+rn+2, or rn+2=rn−qrn+1.

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B) State and prove Euclidean theorem.​

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B) State and prove Euclidean theorem.