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.

  • $\begingroup$ What have you referenced/checked/tried? $\endgroup$ – Eric Towers Jun 25 '14 at 14:51
  • $\begingroup$ No more squares in the first 11000 elements of the sequence (determined by directly generating the numerators and checking for squareness). $\endgroup$ – Eric Towers Jun 25 '14 at 14:55
  • $\begingroup$ yea but the complication lies in the proof. Do you have any idea? $\endgroup$ – Amber Ji Jun 25 '14 at 15:01
  • 1
    $\begingroup$ 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. $\endgroup$ – user155234 Jun 25 '14 at 21:55
  • 1
    $\begingroup$ @Albert thats the problem i got $\endgroup$ – Amber Ji Jun 27 '14 at 16:50

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.