Why does the Diophantine equation $6xy-3x-2y+1=0$ have no solution in $ \mathbb{Z}^2$?

Question

Consider the function $f(x,y)= 6xy-3x-2y+1$.

Question: Why does the Diophantine equation $f(x,y)=0 $ have no solution in $ \mathbb{Z}^2$?

I have seen a few questions like this on this page..but still couldn't figure out what the trick is here..

appreciate any help!

You should use correct spelling – Kishalay Sarkar Nov 27 '19 at 08:42 — Kishalay Sarkar, Nov 27 '19 at 08:42

score 3 · Accepted Answer · answered Nov 27 '19 at 08:42

3

$f(x,y)=(3x-1)(2y-1)$ is this is $0$ only when $x=\frac 1 3$ or $y=\frac 1 2$.

answered Nov 27 '19 at 08:42

Kavi Rama Murthy

6

Please strive not to post further dupe answers to FAQs - this complicates site organization. – Bill Dubuque Nov 27 '19 at 14:04

1 Answers1