Problem: Prove that there are infinitely many natural numbers that can't be written as $6xy+x+y$ where $x,y$ are positive integers.
I noticed that if $A=6xy+x+y$ then $6A+1=(6x+1)(6y+1)$, but I can't proceed from here. A hint would be great!
Problem: Prove that there are infinitely many natural numbers that can't be written as $6xy+x+y$ where $x,y$ are positive integers.
I noticed that if $A=6xy+x+y$ then $6A+1=(6x+1)(6y+1)$, but I can't proceed from here. A hint would be great!
Hint:
Prime is infinite of form $6k+1$ where $k$ is an integer and prime cannot be written as two product.