Question

Irrationality of $\sum\limits_{n=1}^{\infty} r^{-n^{2}}$ for every integer $r > 1$

score 195 · Answer 1 · 2017-02-04 10:57:15

195

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Irrationality of $\sum\limits_{n=1}^{\infty} r^{-n^{2}}$ for every integer $r > 1$

Published on 04 Feb 2017 - 10:57

score 9.4k · Answer 2 · 2017-02-06 11:47:50

9.4k

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Limit points of irrationals

Published on 06 Feb 2017 - 11:47

score 214 · Answer 3 · 2017-02-07 20:46:33

214

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Prove that this iteration cuts a rational number in two irrationals $\sum_{n=0}^\infty \frac{1}{q_n^2-p_n q_n+1}+\lim_{n \to \infty} \frac{p_n}{q_n}$

Published on 07 Feb 2017 - 20:46

score 892 · Answer 4 · 2026-03-27 13:27:20

892

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Is this formula for $\frac{e^2-3}{e^2+1}$ known? How to prove it?

Published on 27 Mar 2026 - 13:27

score 330 · Answer 5 · 2026-03-26 22:57:54

330

Views

$\sqrt{2} \notin \mathbb{Q}$ and Galois Cohomology

Published on 26 Mar 2026 - 22:57

score 5.7k · Answer 6 · 2017-02-09 09:13:54

5.7k

Views

Why no common factors in proving root 2 is irrational?

Published on 09 Feb 2017 - 9:13

score 1.6k · Answer 7 · 2017-02-11 05:35:25

1.6k

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Prove, by contradiction, that, if $cx^2 + bx + a$ has no rational root, then $ax^2 + bx + c$ has no rational root.

Published on 11 Feb 2017 - 5:35

score 794 · Answer 8 · 2017-02-11 22:25:32

794

Views

Is sum of roots of 2 always irrational?

Published on 11 Feb 2017 - 22:25

score 1.4k · Answer 9 · 2026-03-26 09:41:03

1.4k

Views

Properties of Irrational and Rational Numbers

Published on 26 Mar 2026 - 9:41

score 867 · Answer 10 · 2017-02-15 09:28:25

867

Views

Understanding proof that between any two unequal rationals there is a third rational.

Published on 15 Feb 2017 - 9:28

score 90 · Answer 11 · 2026-03-27 08:16:44

90

Views

Is it possible that a non repeating expansion in a variable base to be rational?

Published on 27 Mar 2026 - 8:16

score 609 · Answer 12 · 2017-02-15 15:01:02

609

Views

prove by contradiction that $(p/q)^2 =3$ has no solution

Published on 15 Feb 2017 - 15:01

score 51 · Answer 13 · 2026-03-28 12:33:34

51

Views

Is $\pi$ multiplied by roots of naturals always irrational?

Published on 28 Mar 2026 - 12:33

score 616 · Answer 14 · 2017-02-18 03:51:25

616

Views

Number of correct digits of an expression.

Published on 18 Feb 2017 - 3:51

score 65 · Answer 15 · 2017-02-18 18:28:28

65

Views

a nbe b irrational numbers hnce a^b is rational

Published on 18 Feb 2017 - 18:28

List Question

Irrationality of $\sum\limits_{n=1}^{\infty} r^{-n^{2}}$ for every integer $r > 1$

Limit points of irrationals

Prove that this iteration cuts a rational number in two irrationals $\sum_{n=0}^\infty \frac{1}{q_n^2-p_n q_n+1}+\lim_{n \to \infty} \frac{p_n}{q_n}$

Is this formula for $\frac{e^2-3}{e^2+1}$ known? How to prove it?

$\sqrt{2} \notin \mathbb{Q}$ and Galois Cohomology

Why no common factors in proving root 2 is irrational?

Prove, by contradiction, that, if $cx^2 + bx + a$ has no rational root, then $ax^2 + bx + c$ has no rational root.

Is sum of roots of 2 always irrational?

Properties of Irrational and Rational Numbers

Understanding proof that between any two unequal rationals there is a third rational.

Is it possible that a non repeating expansion in a variable base to be rational?

prove by contradiction that $(p/q)^2 =3$ has no solution

Is $\pi$ multiplied by roots of naturals always irrational?

Number of correct digits of an expression.

a nbe b irrational numbers hnce a^b is rational

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