Use the Euclidean algorithm to find gce(34,126) and write it as a linear combination of 34 and 126.

Tarnayfu

Tarnayfu

Answered question

2022-08-02

Use the Euclidean algorithm to find gce(34,126) and write it as a linear combination of 34 and 126.

Answer & Explanation

kidoceanoe

kidoceanoe

Beginner2022-08-03Added 15 answers

we apply Euclid's algorithm to find the GCD
of given pair of numbers
consider 34, 126
observe that 126 = 34 (3) +24.......(1)
34=24 (1) +10....(2)
24=10 (2) + 4....(3)
10=4 (2) +2....(4)
4=2(2)+0
so (34, 126) = 2
from (4), 2=10 + (-2) 4
= 10+(-2)[24-10(2)] from (3)
=5(10)+(-2)24
=5[34-24(1)]+(-2)24 from (2)
= 5(34)+(-7) 24
=5(34) +(-7)[126-34(3)] from (1)
= 26(34) +(-7) 126
hence 2=26(34) +(-7)126

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