Use the Euclidean Algorithm with back-substitution tofind thegcd(a, b)and then writegcd(a, b) =as+bt,noting the + between the terms witha, b, s, t∈Z. 1.a= 15, b= 26. The answer is1 = 15·7 + 26·(−4), now show the work. 2.a= 25, b= 1234. The answer is1 = 25·(543) + 1234(−11), now show the work.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.5: Congruence Of Integers
Problem 34E
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Use the Euclidean Algorithm with back-substitution tofind thegcd(a, b)and then writegcd(a, b) =as+bt,noting the + between the terms witha, b, s, t∈Z.

1.a= 15, b= 26. The answer is1 = 15·7 + 26·(−4), now show the work.

2.a= 25, b= 1234. The answer is1 = 25·(543) + 1234(−11), now show the work.

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