Question

Find all monic polynomials $f(x)$ having integer coefficients such that $f(0)=2020$ and for any irrational $x$, $f(x)$ is also irrational.

score 453 · Answer 1 · 2026-04-16 10:41:27

453

Views

Find all monic polynomials $f(x)$ having integer coefficients such that $f(0)=2020$ and for any irrational $x$, $f(x)$ is also irrational.

Published on 16 Apr 2026 - 10:41

score 137 · Answer 2 · 2026-04-10 21:12:00

137

Views

How is the "diagonal proof" valid?

Published on 10 Apr 2026 - 21:12

score 106 · Answer 3 · 2026-03-26 17:51:58

106

Views

Which irrationals become rational for some positive integer power?

Published on 26 Mar 2026 - 17:51

score 523 · Answer 4 · 2026-04-09 10:08:05

523

Views

Prove that the sum $ \sqrt{1001^2 + 1}+\sqrt{1002^2 + 1} \ + ... + \sqrt{2000^2 + 1}$ is irrational

Published on 09 Apr 2026 - 10:08

score 120 · Answer 5 · 2026-04-17 05:16:45

120

Views

Number of irrational coordinates of the circle $x^2+y^2=5$.

Published on 17 Apr 2026 - 5:16

score 49 · Answer 6 · 2026-04-09 17:42:55

49

Views

How to express any irrational number in radicals as a trigonometric expression

Published on 09 Apr 2026 - 17:42

score 177 · Answer 7 · 2026-04-16 07:36:32

177

Views

INMO : Prove that $\sqrt[3]{a}$ and $\sqrt[3] {b}$ themselves are rational numbers

Published on 16 Apr 2026 - 7:36

score 220 · Answer 8 · 2026-04-11 22:29:15

220

Views

Quadratic irrationals with continued fraction of period one

Published on 11 Apr 2026 - 22:29

score 23 · Answer 9 · 2026-04-17 07:24:05

23

Views

Irrationality of a real number $b$ that is related to a real number $a$ by the umbral Taylor series.

Published on 17 Apr 2026 - 7:24

score 97 · Answer 10 · 2026-04-11 20:40:28

97

Views

Can an irrational number be expressed as a sum of other irrational numbers, at least one of which is not an integral multiple of the required number?

Published on 11 Apr 2026 - 20:40

score 105 · Answer 11 · 2026-04-08 20:23:11

105

Views

What is the term for 'PI-indexing'?

Published on 08 Apr 2026 - 20:23

score 402 · Answer 12 · 2026-04-13 05:05:34

402

Views

Proof of $\pi^e$ and $e^\pi$ Being Irrational

Published on 13 Apr 2026 - 5:05

score 443 · Answer 13 · 2026-04-30 06:47:37

443

Views

Greedy algorithm Egyptian fractions for irrational numbers - patterns and irrationality proofs

Published on 30 Apr 2026 - 6:47

score 205 · Answer 14 · 2026-04-15 21:41:50

205

Views

Notation for representing ANY number?

Published on 15 Apr 2026 - 21:41

score 220 · Answer 15 · 2026-04-12 12:17:28

220

Views

$\pi$ and $e$ as coded trajectories

Published on 12 Apr 2026 - 12:17

List Question

Find all monic polynomials $f(x)$ having integer coefficients such that $f(0)=2020$ and for any irrational $x$, $f(x)$ is also irrational.

How is the "diagonal proof" valid?

Which irrationals become rational for some positive integer power?

Prove that the sum $ \sqrt{1001^2 + 1}+\sqrt{1002^2 + 1} \ + ... + \sqrt{2000^2 + 1}$ is irrational

Number of irrational coordinates of the circle $x^2+y^2=5$.

How to express any irrational number in radicals as a trigonometric expression

INMO : Prove that $\sqrt[3]{a}$ and $\sqrt[3] {b}$ themselves are rational numbers

Quadratic irrationals with continued fraction of period one

Irrationality of a real number $b$ that is related to a real number $a$ by the umbral Taylor series.

Can an irrational number be expressed as a sum of other irrational numbers, at least one of which is not an integral multiple of the required number?

What is the term for 'PI-indexing'?

Proof of $\pi^e$ and $e^\pi$ Being Irrational

Greedy algorithm Egyptian fractions for irrational numbers - patterns and irrationality proofs

Notation for representing ANY number?

$\pi$ and $e$ as coded trajectories

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