# simple hyperbolic Diophantine equation [closed]

How can we show that there are infinitely many integers $C$ such that the simple hyperbolic diophantine equation: $$6xy ± x ± y = C$$ gives a non-integer solutions for $x, y$, except at $(0, ±C), (±C,0)$?

Some of these values of $C = \{3,5,7,10,…\}$.

## closed as off-topic by Xander Henderson, Jendrik Stelzner, Brahadeesh, José Carlos Santos, TaroccoesbroccoAug 6 '18 at 8:21

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, Jendrik Stelzner, Brahadeesh, José Carlos Santos, Taroccoesbrocco
If this question can be reworded to fit the rules in the help center, please edit the question.