# Wolstenholme Number

A Wolstenholme number is the (reduced) numerator of the fraction $$1+{1\over4}+\cdots+{1\over n^2}$$. The first few are $$1, 5, 49, 205, 5269, 5369, 266681, 1077749$$.

Are there Wolstenholme numbers that are perfect squares other than $$1$$ and $$49$$?

Seems to be a complicated problem.

• What have you referenced/checked/tried? – Eric Towers Jun 25 '14 at 14:51
• No more squares in the first 11000 elements of the sequence (determined by directly generating the numerators and checking for squareness). – Eric Towers Jun 25 '14 at 14:55
• yea but the complication lies in the proof. Do you have any idea? – Amber Ji Jun 25 '14 at 15:01
• I tried looking it up in teh oeis, I got A007406. then i tried lookign up 1, 49 and got almost fore hundred results. google isnt much help cause their's a Wolstehnolme Square in London. – user155234 Jun 25 '14 at 21:55
• @Albert thats the problem i got – Amber Ji Jun 27 '14 at 16:50