leshik
Reputation
4,305
Top tag
Next privilege 5,000 Rep.
Approve tag wiki edits
 Sep 26 reviewed Approve The solution of $\min_x \max_{1\leq r \leq N} \left|\frac{\sin rMx}{\sin rx}\right|$ Aug 30 awarded Yearling Jul 25 awarded Revival 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 $f(2)\ge f(1)$ 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