Question

What are the necessary conditions for a polynomial Q(X) such that the roots of Q(X) - X are equal to the real roots of a polynomial P?

score 206 · Answer 1 · 2026-03-25 15:12:10

206

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What are the necessary conditions for a polynomial Q(X) such that the roots of Q(X) - X are equal to the real roots of a polynomial P?

Published on 25 Mar 2026 - 15:12

score 25 · Answer 2 · 2026-04-12 22:39:20

For which Z-irreducible polynomials is there a nonconstant polynomial with coefficients in {-1,0,1} equivalent to +/- 1?

score 123 · Answer 3 · 2026-04-06 14:20:24

123

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Maximum number of algebraically independent homogeneous polynomials of given degree

Published on 06 Apr 2026 - 14:20

score 51 · Answer 4 · 2026-04-12 17:33:41

51

Views

Polynomial P equals to 0

Published on 12 Apr 2026 - 17:33

score 664 · Answer 5 · 2026-04-11 20:36:28

664

Views

Bounding a polynomial from below

Published on 11 Apr 2026 - 20:36

score 112 · Answer 6 · 2026-03-29 18:32:22

112

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Coefficients of $(1+x+x^2)^{2018}$

Published on 29 Mar 2026 - 18:32

score 48 · Answer 7 · 2026-04-13 15:47:35

48

Views

If two polynomials share a root, does their sum/product also share that root?

Published on 13 Apr 2026 - 15:47

score 30 · Answer 8 · 2019-03-20 02:58:43

Conditions for $\sum\limits_{n=0}^{N}\sum\limits_{k=0}^{K}\Bigl[a_{n,k}\prod\limits_{i=1-k}^{I}(x+i)\prod\limits_{j=1-n}^{J}(x+j)\Bigr]$ to be $0$

score 116 · Answer 9 · 2026-04-12 12:59:35

116

Views

Complex analysis, P(z)

Published on 12 Apr 2026 - 12:59

score 661 · Answer 10 · 2026-04-12 17:33:30

661

Views

Polynomial and prime factors

Published on 12 Apr 2026 - 17:33

score 32 · Answer 11 · 2026-03-25 08:14:30

32

Views

Solving equation of form $a = \prod_i^N (c_i e^t + b)^{c_i}$

Published on 25 Mar 2026 - 8:14

score 263 · Answer 12 · 2019-03-21 05:09:20

263

Views

Show that for infinitely many pairs of $(a,b)$ for $x^2+ax+b=0$ and $x^2+2ax+b=0$ have integer roots.

Published on 21 Mar 2019 - 5:09

score 86 · Answer 13 · 2026-03-25 16:48:54

86

Views

Associated primes of the square of a monomial ideal

Published on 25 Mar 2026 - 16:48

score 137 · Answer 14 · 2026-04-13 01:25:56

137

Views

GCD of cubic polynomials

Published on 13 Apr 2026 - 1:25

score 102 · Answer 15 · 2019-03-21 16:45:18

102

Views

How to find irreducible factors of the polynomial $p(x) = x^5 -1$ over integers modulo $5$

Published on 21 Mar 2019 - 16:45

List Question

What are the necessary conditions for a polynomial Q(X) such that the roots of Q(X) - X are equal to the real roots of a polynomial P?

For which Z-irreducible polynomials is there a nonconstant polynomial with coefficients in {-1,0,1} equivalent to +/- 1?

Maximum number of algebraically independent homogeneous polynomials of given degree

Polynomial P equals to 0

Bounding a polynomial from below

Coefficients of $(1+x+x^2)^{2018}$

If two polynomials share a root, does their sum/product also share that root?

Conditions for $\sum\limits_{n=0}^{N}\sum\limits_{k=0}^{K}\Bigl[a_{n,k}\prod\limits_{i=1-k}^{I}(x+i)\prod\limits_{j=1-n}^{J}(x+j)\Bigr]$ to be $0$

Complex analysis, P(z)

Polynomial and prime factors

Solving equation of form $a = \prod_i^N (c_i e^t + b)^{c_i}$

Show that for infinitely many pairs of $(a,b)$ for $x^2+ax+b=0$ and $x^2+2ax+b=0$ have integer roots.

Associated primes of the square of a monomial ideal

GCD of cubic polynomials

How to find irreducible factors of the polynomial $p(x) = x^5 -1$ over integers modulo $5$

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