New posts in rational-numbers

Prove that the square root of any irrational number is irrational.

Is there a definition of a "pseudo period" for $f(x)=\sin(3x)+\sin(\pi x)$?

How can I show the sets are open? (The set of rational numbers $\mathbb{Q}$ is not a connected topological space)

Compute the kernel of the group hom $\Omega : \Bbb{Q}^{\times} \to \Bbb{Z}^+$.

Rational numbers as vectors in infinite dimensional space with the basis $( \log 2,\log 3, \log 5, \log 7, \dots, \log p, \dots) $

How to obtain all the rational numbers without repetitions?

Does there exist a bijection $f$ from $\mathbb{N}$ to $\mathbb{Q}^+$ such that $\lim_{n \to \infty} \frac{f(n+1)}{f(n)}$ exists?

Proving that the Calkin-Wilf tree enumerates the rationals.

Pondering $f(x) = \alpha x$ for an irrational $\alpha$.

When is an Integer a Rational Number, and are All Ratios Rational, Even $\frac{\sqrt{7}}{2}$?

Find minimum $n$ for $x^2+3x+6=f_1(x)^2+f_2(x)^2+ \cdots +f_n(x)^2$

Which is greater: $1000^{1000}$ or $1001^{999}$

Is $\frac{\zeta (m+n)}{\zeta (m)\zeta (n)}$ a rational number for $m,n\ge 2\in\mathbb N$?

Prove that x is rational

Linear Diophantine equations with fractional coefficients

Variation in density of the Farey sequence in the interval $[0,1]$

If $a^4+b^4\in\mathbb Q$ and $a^3+b^3\in\mathbb Q$ and $a^2+b^2\in\mathbb Q$, prove that $a+b\in\mathbb Q$ and $ab\in\mathbb Q$.

Rational root theorem

For what algebraic curves do rational points form a group?

For $A \in \mathcal{M}_3(\mathbb{C})$, does $\mathrm{tr}(A^2) = \mathrm{tr}(A^3) \in \mathbb{Q}$ imply $\mathrm{tr}(A^4) \in \mathbb{Q}$?