Question

For any neZ^+, prove that the integers 8n +3 and 5n+2 are relatively prime. Compute the multipliers to compute inverse of one number with respect to the other number.

Answer 1

Answer:

See step-by-step explanation below

Step-by-step explanation:

This problem is solved using the Euclidean algorithm; to prove that the integers 8n + 3 and 5n + 2 are relative prime we have to prove that:

gcd(8n + 3, 5n + 2) = 1

gcd (8n + 3, 5n + 2) = gcd (3n + 1, 5n + 2) = gcd (3n + 1, 2n + 1) = gcd(n, 2n + 1) = gcd(n,1) = 1

⇒gcd(8n + 3, 5n + 2) = 1