Unformatted text preview: k . Problem 3. Use the Extended Euclidean Algorithm 2.25 to compute d = gcd(3953 , 1829) and then ﬁnd two diﬀerent pairs x,y ∈ Z such that 3953 x + 1829 y = d . Problem 4. We say a,b ∈ Z are coprime if gcd( a,b ) = 1. For all a,b,c ∈ Z prove that ab is coprime to c if and only if a and b are both coprime to c . (Hint: Use the GCD Characterization Theorem 2.24.) Problem 5. Prove that there is no perfect square of the form 4 k + 3....
View Full Document
- Fall '11
- Math, Greatest common divisor, Euclidean algorithm, 4k, Extended Euclidean algorithm, GCD Characterization Theorem, Drew Armstrong