Question

- prove that for every n natural numbers grater or equal 2 exist one p and k numbers prim grater or equal 2 such that the below equation is true :

(p-1) (k-1)
----- + ----- +1 = n
2 2

Answer 1

for example :

(2-1) (2-1)
----- + ------ +1 = 2
2 2

Answer 2

(3-1) (3-1)
----- + ----- +1 =3
2 2

Answer 3

(5-1) (3-1)
----- + ----- +1 = 2 +1 +1 =4
2 2

Answer 4

(5-1) (5-1)
----- + ----- +1 = 2+2+1=5
2 2

Answer 5

can be this proven that is true for every natural numbers ?