Solution :
Step one – use the Euclidean algorithm
(1) 149 = 1 × 139 + 10
(2) 139 = 13 × 10 + 9
(3) 10 = 1 × 9 + 1
(4) 9 = 9 × 1 + 0
(5)
A remainder of 0 has been obtained, so the gcd is the last non-zero remainder, hence
gcd(149,139) = 1 as required.
Step two – rearrange the earlier expressions to make the remainder the subject.
(3) 1 = 10 – 1 × 9
(2) 9 = 139 – 13 × 10
(1) 10 = 149 – 1 × 139
Step 3 – back substitute
Start with (3) 1 = 10 [× 1] – 1 × 9
Substitute in (2) 1 = 10 × 1 – 1(139 – 13 × 10)
1 = 10 × 1 – 139 × 1 + 13 × 10
1 = 10 × 14 – 139 × 1
Substitute in (1) 1 = (149 × 1 – 1 × 139) × 14 – 139 × 1
1 = 149 × 14 – 14 × 139 – 139 × 1
1 = 149 × 14 – 15 × 139
Thus,149u + 139v = 1 ;where u = 14 and v = –15.
Use Euclidean algorithm to find integers u and v such that 149u + 139V = 1,...
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To use the Euclidean algorithm to find the greatest counen divisor of each pair of integers' © 2041, 9614 lü) 490256, 674
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