Let k elementof Z Show that gcd 4k 2 k2 k 2Solution4k2 k

Let k elementof Z. Show that gcd (4k + 2, k^2 + k) = 2.

Solution

4k+2 | k² + k | k/4

k² + k/2

.................................

0 + k/2 | 4k+2 | 8

4k

......................................

2 | k/2 | k/4

k/2

.......................................................

0

therefore , 2 is GCD