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 23 What is sum of all positive odd integers less than $1000$? 16 Proving a relation between $\sum\frac{1}{(2n-1)^2}$ and $\sum \frac{1}{n^2}$ 12 Determine splitting field $K$ over $\mathbb{Q}$ of the polynomial $x^3 - 2$ 11 Show that $n \ge \sqrt{n+1}+\sqrt{n}$ 9 How to prove this inequality $\frac{x^y}{y^x}+\frac{y^z}{z^y}+\frac{z^x}{x^z}\ge 3$

### Reputation (619)

 +10 The n-th root of a prime number is irrational +10 Determine splitting field $K$ over $\mathbb{Q}$ of the polynomial $x^3 - 2$ +10 When is the inequality $\beta(a_1+b_1, a_2+b_2)\ge \beta(a_1, a_2)\beta(b_1, b_2)$ true? +10 Sum of two independent binomial variables

### Questions (4)

 6 If $q$ is prime, then $w=(1+q+q^2)/3$ is a composite integer iff $w$ has a prime divisor less than $\sqrt{w}$ and congruent to $1$ modulo $6$ 4 Determining a confidence interval for $\sigma$ from a Rayleigh distribution 4 $N_Q(R)=N_Q(Q\cap R)$ where $Q, R \le P$, $Q$ normal and $P$ a $p$-group 2 When is the inequality $\beta(a_1+b_1, a_2+b_2)\ge \beta(a_1, a_2)\beta(b_1, b_2)$ true?

### Tags (43)

 50 algebra-precalculus × 4 12 irreducible-polynomials 24 summation × 2 12 field-theory 20 inequality × 3 12 splitting-field 16 sequences-and-series × 2 12 roots-of-unity 13 induction × 4 11 linear-algebra × 3

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