« first day (138 days earlier)      last day (240 days later) » 

Sophie
Sophie
9:33 AM
I put a bounty on this question, it expires tomorrow and I haven't got any answers math.stackexchange.com/questions/2042839/…
 
Martin Sleziak
Martin Sleziak
@Sophie The room is intended for bounties which already ended, and the user is still interested in the question (and willing to reward answerers if an answer fulfilling their requirements is posted). See the rules described here.
But I don't think that there is too much harm in posting it here a bit prematurely - if it gets no answer until tomorrow it will fulfill the criteria.
I will post it once again, just oneboxed:
8
Q: Solutions to the diophantine equation $x^n-2y^n=1$. Can the sum of the first $n$ squares be a perfect power?

SophieThis is an attempt to generalize this question. $$x^n-2y^n=1\implies \frac{x}{y}=\left(2+\frac{1}{y^n}\right)^{\frac 1 n}=2^\frac1n\left(1+\frac{1}{2y^n}\right)^\frac1n<2^\frac 1n\left(1+\frac{1}{2ny^n}\right)$$ $$0<\frac{x}{y}-2^\frac1n<\frac{2^\frac1n}{2ny^n}$$ but since the irrationality meas...

number-theory diophantine-equations diophantine-approximation
Basically in this post on meta I suggested that we create some place for the bounties which already ended and the OP is still not satisfied with the answer (or did not get any answers). This room is an attempt to create such place.
The bounties which are still active receive additional attention because they are in the featured tab. And the plan is that from here also the past bounties question - which are no longer on that tab - could get some additional views and possibly, in some cases, also an answer.
 

« first day (138 days earlier)      last day (240 days later) »