# Solving a diophantine equation in an elementary way

I was trying to solve $x^2+1=y^3$ and found this answer: Does an elementary solution exist to $x^2+1=y^3$?

but I'm having trouble understanding it.

In the second last paragraph, why is there a contradiction ($\textrm{mod}\ 49$) ?

Any help would be much appreciated.

• This is Mordell's equation. For elementary solutions, see here. See also the references here. – Dietrich Burde Jun 5 '15 at 17:46
• @Dietrich Burde I know what mordell equation is but I'm specifically interested in Slade's solution. – sacch Jun 6 '15 at 0:53
• I see - you can ask him perhaps (with a comment below his answer). – Dietrich Burde Jun 6 '15 at 8:51
• I read this question and spent some time reading Slade's answer, and I couldn't get it either. I've dropped him a comment. – shardulc says Reinstate Monica Jun 6 '15 at 20:52
• @shardulc Thanks a lot! I hope he could fix his answer because I really like his solution. – sacch Jun 9 '15 at 14:19