# Hecke

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bio website location age member for 11 months seen 2 hours ago profile views 1,828

I'm interested in number theory, especially in diophantine equations.

# 89 Questions

 84 Can $x^{x^{x^x}}$ be a rational number? 36 Does the sum $\sum_{n=1}^{\infty}\frac{\tan n}{n^2}$ converge? 25 Find $a,b,c,d,e$ such that $\dfrac{s}a+1,\dfrac{s}b+1,\dfrac{s}c+1,\dfrac{s}d+1,\dfrac{s}e+1$ are all perfect squares $(s=abcde)$ 19 Sum involving binomial coefficient satisfies congruence (A contest question) 17 $x^3-3x-3=0$, prove that $10^x<127$

# 5,824 Reputation

 +5 Does the sum $\sum_{n=1}^{\infty}\frac{\tan n}{n^2}$ converge? +5 Are there examples that we know a number is a rational number but we do not know what is its numerator and denominator? +5 Can $x^{x^{x^x}}$ be a rational number? +5 Find $a,n\in \mathbb N^{+}:a!+\dfrac{n!}{a!}=x^2,x\in \mathbb N$

 23 How to prove there are no more positive integers that are products of 2 and 3 consecutive numbers? 18 Pythagorean triplets $x^2+y^2 = z^3$ 13 Find integer in the form: $\frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b}$ 12 Does there exist rational $a,b,c$, such that $\sqrt[3]{1}+\sqrt[3]{2}+\sqrt[3]{4}=\sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}$ 8 How prove this $\sqrt[5]{1782+\sqrt[3]{35+15\sqrt{6}}+\cdots}$ is positive integer numbers.

# 72 Tags

 172 number-theory × 106 15 abstract-algebra × 4 62 diophantine-equations × 29 13 elliptic-curves × 4 61 elementary-number-theory × 51 11 contest-math × 4 23 computer-science 9 arithmetic × 3 19 algebra-precalculus × 5 8 calculus × 3

# 1 Account

 Mathematics 5,824 rep 2744