Solving a diophantine equation in an elementary way

Asked Jun 05 '15 at 15:15

Active Jun 05 '15 at 15:30

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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.

edited Jun 05 '15 at 15:30

muaddib

asked Jun 05 '15 at 15:15

sacch

This is Mordell's equation. For elementary solutions, see here. See also the references here. – Dietrich Burde Jun 05 '15 at 17:46
@Dietrich Burde I know what mordell equation is but I'm specifically interested in Slade's solution. – sacch Jun 06 '15 at 00:53
I see - you can ask him perhaps (with a comment below his answer). – Dietrich Burde Jun 06 '15 at 08:51
1

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 Jun 06 '15 at 20:52
@shardulc Thanks a lot! I hope he could fix his answer because I really like his solution. – sacch Jun 09 '15 at 14:19
Stan Dolan contributed a really lovely — and completely elementary — solution on the linked post. – Kieren MacMillan Jul 07 '21 at 20:15

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