Show that $ 5*n + 3 $ and $ 7*n + 4 $ are relatively prime. $ 7*n + 4 = 5*n + 3 + 2*n + 1 5*n + 3 = 2*(2*n + 1) + n + 1 2*n + 1 = 1*(n + 1) + n n + 1 = 1*n + 1 $
After constant long division we get to the base equation where there is still a remainder of 1. Therefore $ 5*n + 3 $ and $ 7*n + 4 $ are relatively prime.
