Can $a(2as-4a-s-4)$ be a prime, except when $a=1$

Question

Can $a(2as-4a-s-4)$ be a prime, except when $a=1$. And both $a$ and $s$ are positive integers

No, since it's divisible by $a$. – AnotherTest Nov 19 '15 at 18:27 — AnotherTest, Nov 19 '15 at 18:27
no because you multiply by $a$ – Zelos Malum Nov 19 '15 at 18:27 — Zelos Malum, Nov 19 '15 at 18:27

score 3 · Accepted Answer · answered Nov 19 '15 at 18:32

3

No because $$2as-4a-s-4=1\iff (2a-1)(s-2)=7$$ $$\iff (a,s)=(1,9),(4,3)$$

answered Nov 19 '15 at 18:32

mathlove

This answer assumes that in order for a number to be prime, it must be positive (which, depending on your conventions, may or may not be the case). On the other hand, if primes are allowed to be negative, then $(a,s) = (3,3)$ gives the answer $-3$, which is prime. (And using mathlove's same steps one can show that it is the only answer). – Jason DeVito - on hiatus Nov 19 '15 at 18:42

1 Answers1