Let’s divide the odd positive integers into two arithmetic progressions; the red numbers are 1, 5, 9, 13, 17, 21, ... The blue numbers are 3, 7, 11, 15, 19, 23, a. Prove that the product of two red numbers is red, and that the product of two blue numbers is red.
b. Prove that every blue number has a blue prime factor.
c. Prove that there are infinitely many blue prime numbers.