Problem 12
Find the greatest common divisor of each pair of integers. $$ 0,17 $$
Problem 12
Use the Euclidean algorithm to find the greatest common divisor of each pair of integers. $$ 57853125,555111200 $$
Problem 13
Express each binary number in decimal. $$ 11011011 $$
Problem 14
Express each binary number in decimal. $$ 100000 $$
Problem 15
Find the greatest common divisor of each pair of integers. $$ 110,273 $$
Problem 26
Add the binary numbers. $$ 101101+11011 $$
Problem 26
Suppose that \(d>0\) is a common divisor of nonnegative integers \(a\) and \(b\), not both zero. Prove that \(d \mid \operatorname{gcd}(a, b)\).
Problem 27
Show that if \(p\) is a prime number, \(a\) and \(b\) are positive integers, and \(p \mid a b,\) then \(p \mid a\) or \(p \mid b\).
Problem 39
Show that \(\operatorname{gcd}(n, \phi)=1,\) and find the inverse s of \(n\)
modulo \(\phi\) satisfying \(0
Problem 40
Show that \(\operatorname{gcd}(n, \phi)=1,\) and find the inverse s of \(n\)
modulo \(\phi\) satisfying \(0