Reputation
4,190
Top tag
Next privilege 5,000 Rep.
Approve tag wiki edits
Badges
1 5 14
Newest
 Tumbleweed
Impact
~30k people reached

Feb
10
awarded  Tumbleweed
Feb
3
comment For positive $x,y$ such that $x+y \leq x^2+y^2$ prove inequality for every real $t \ge 1$ $x^t+y^t \leq x^{t+1}+y^{t+1}$.
$x+y\ge 2$ is not always true. Just take $y$ close to $0$ and say $x=\frac{3}{2}.$ As to the general problem: one may consider the function $f(t)=\log (x^t+y^t)$ and use it convexity that follows from Cauchy- Swartz together with the observation that $f(2)\ge f(1)$
Feb
3
revised Solutions of Pell's equation of the special form
added 162 characters in body
Feb
3
asked Solutions of Pell's equation of the special form
Jan
27
comment Polynomial/ Exponential diophantine equation
Thanks Will! In case quadratic function is a complete square, we can have infinitely many solutions. But this together with your characterization covers all cases indeed. I think I will just cite Siegel work.
Jan
27
comment Polynomial/ Exponential diophantine equation
i've added the clarification. Here, $a,b,c$ are fixed whereas $m,n$ vary
Jan
27
revised Polynomial/ Exponential diophantine equation
added 6 characters in body
Jan
27
asked Polynomial/ Exponential diophantine equation
Dec
10
awarded  Caucus
Nov
17
answered Bounding error of Padé approximation
Aug
30
awarded  Yearling
Aug
28
comment Prove that $\sum \limits_{d|n}(n/d)\sigma(d) = \sum \limits_{d|n}d\tau(d)$
both sides are multiplicative functions. So it is enough to check the equality for prime powers
Jul
1
comment Resources about infinite primes of form $n^2 + 1$
Look at this post math.stackexchange.com/questions/44126/… The best partial progress for the polynomial values that are prime (in two dimensions though) is the work of Iwaniec and Friedlander en.wikipedia.org/wiki/Friedlander–Iwaniec_theorem
Jul
1
comment Resources about infinite primes of form $n^2 + 1$
the problem is open. You want resources that contain partial progress?
Jun
28
answered How prove this Stronger AM-GM inequality $\frac{n^2-1}{6}\min_{1\le i<j\le n}\left(\sqrt{a_{i}}-\sqrt{a_{j}}\right)^2\le A_{n}-G_{n}$
Jun
27
revised Integer values of $\frac{x}{y}+\frac{y}{z}+\frac{z}{x}$?
added 1 character in body
Jun
27
revised Integer values of $\frac{x}{y}+\frac{y}{z}+\frac{z}{x}$?
added 217 characters in body
Jun
27
revised Integer values of $\frac{x}{y}+\frac{y}{z}+\frac{z}{x}$?
added 300 characters in body
Jun
27
revised Integer values of $\frac{x}{y}+\frac{y}{z}+\frac{z}{x}$?
added 300 characters in body
Jun
27
answered Integer values of $\frac{x}{y}+\frac{y}{z}+\frac{z}{x}$?