Let A = {4k +1 | k ∈

**Z^+**}. Show that there exists a prime

*p*of A, and elements

*j, k,*of A, such that

*p*| (

*jk*), but

*p*does not divide

*j*or

*k.*

In words: "Let A equal the set of elements of 4k+1, where k is an element of all positive integers. Show that there exists a prime p of A, and elements j, k of A, such that p divides j times k, but p does not divide j OR k"

I am aware that this equation (4k+1) does not have a Unique Factorization Property, but I am not sure if that has anything to do with the problem.