[seqfan] Problem with difference of squares

Georgi Guninski guninski at guninski.com
Fri Jan 28 08:14:17 CET 2011

n \neq m \neq 0
n,m squarefree

Can the number of solutions in Z be unbounded as n,m vary?

I suppose if the squarefree restriction is dropped the answer is yes via elliptic curves.

Any heuristics?

Probably the question is an open problem.

A possible relaxation might be replacing n,m with c_1 n, c_2 m with small c_1,c_2.



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