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Feb
8
reviewed Leave Closed I am looking for a general solution for when $n$ and a rational function $f (n)$ are both integers
Feb
3
comment Interuniversal Teichmuller theory's applications
As far as I know, no.
Jan
31
reviewed No Action Needed Automorphic representations whose local factors are tempered almost everywhere
Jan
31
reviewed Close parametrizing a conic in $F_p$
Jan
31
comment The sequence $a_{n+1}=\left\lceil \frac{-1+\sqrt{5}}{2}a_{n}-a_{n-1} \right\rceil$ is periodic
I still think this should not be on MO. It may be a hard problem but is not a research problem, i.e., I doubt it arose independently in jack's research. Second, I assume whoever posed the problem in the competition (plus, I hope, some of the competitors) know how to solve it, so asking them and not MO is a more efficient way of getting the answer.
Jan
26
comment The Sato-Tate conjecture (Frobenius eigenvalues)
When the elliptic curve has CM by a class number one ring then the eigenvalues of Frobenius are $\pm \sqrt{p}$ for the inert primes and $\pi,\bar{\pi}$ if $p$ factors as $\pi \bar{\pi}$ in the ring.
Jan
8
comment Solving Non-Linear Equations over a Finite Field of a Large Prime Order
@Adam Yes. $ $ $ $
Jan
5
reviewed Close How to cite authors from any country correctly?
Jan
4
revised Solving Non-Linear Equations over a Finite Field of a Large Prime Order
added 120 characters in body
Jan
4
answered Solving Non-Linear Equations over a Finite Field of a Large Prime Order
Jan
3
reviewed Close Does differentiation widen, or narrow, the class of functions?
Dec
30
reviewed Close A linear combination problem
Dec
29
comment Reduced resultant of monic polynomials
Are you asking the same questions as in here: mathoverflow.net/questions/17501/… ?
Dec
27
answered Rational points on towers of curves
Dec
24
reviewed Leave Open Conics, rational points and probability
Dec
20
reviewed Approve limits-and-colimits tag wiki excerpt
Dec
20
reviewed No Action Needed Which finite p-groups occur as commutators of finite p-groups?
Dec
19
comment Existence of pencils on some special curves of genus 10
AKA Castelnuovo-Severi inequality.
Dec
18
comment Does Mochizuki's proof of abc conjecture gives an upper bound for the quality of a triple?
The answer is no, according to Mochizuki.
Dec
16
comment A quadratic Diophantine equation
This curve has $p \pm 1$ points depending on what happens at infinity, as long as it's smooth (i.e. $p \ne 2,5$). There are many simple proofs of this or one can appeal to the Weil bounds. To find a solution, pick $x$ at random and solve for $y$, there is a 50% chance that a given $x$ succeeds. To solve for $y$ you can use the quadratic formula. To take square roots modulo $p$ using one of the known algorithms (google will help).