Question

Is this valid? $r_1^3+r_2^3+\cdots+r_7^3=(r_1+\cdots + r_7)^3-3(r_1+\cdots+r_7)(r_1r_2+r_1r_3+\cdots+r_6r_7)+3(r_1r_2r_3+r_1r_2r_4+\cdots+r_5r_6r_7)$

score 97 · Answer 1 · 2026-03-25 17:26:52

97

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Is this valid? $r_1^3+r_2^3+\cdots+r_7^3=(r_1+\cdots + r_7)^3-3(r_1+\cdots+r_7)(r_1r_2+r_1r_3+\cdots+r_6r_7)+3(r_1r_2r_3+r_1r_2r_4+\cdots+r_5r_6r_7)$

Published on 25 Mar 2026 - 17:26

score 97 · Answer 2 · 2026-04-16 04:25:19

97

Views

Poweriteration for polynomials with roots that have the same absolute value

Published on 16 Apr 2026 - 4:25

score 92 · Answer 3 · 2026-03-25 16:39:24

92

Views

Solution works for 2nd degree polynomial but does not extend to higher degrees.

Published on 25 Mar 2026 - 16:39

score 57 · Answer 4 · 2026-04-09 13:34:28

57

Views

Root representation using the factorization of polynomials upto degree six

Published on 09 Apr 2026 - 13:34

score 65 · Answer 5 · 2026-04-12 14:32:05

65

Views

Why isn't this root equation working out?

Published on 12 Apr 2026 - 14:32

score 72 · Answer 6 · 2026-03-25 08:01:49

72

Views

Do $p_n$ minus the number of integer solutions to this equation equal $(-1)^{\frac{1}{24} \left((p_n){}^2-1\right)}$ for $n>4$?

Published on 25 Mar 2026 - 8:01

score 292 · Answer 7 · 2026-03-25 07:41:58

292

Views

Complex argument in Chebyshev polynomials of second kind?

Published on 25 Mar 2026 - 7:41

score 51 · Answer 8 · 2026-04-12 18:59:03

51

Views

Finding fixed points of a specific constrained nonlinear PDE

Published on 12 Apr 2026 - 18:59

score 87 · Answer 9 · 2026-04-17 15:55:28

87

Views

Consider the curves $C_1: x^2y^2-a^2(x^2+y^2)=0, C_2: xy=a^2, C_3: x^2+y^2=a^2(a≠0).$ Count the number of points & tangents common to all three curves

Published on 17 Apr 2026 - 15:55

score 32 · Answer 10 · 2026-04-13 22:28:20

32

Views

Can these two concave functions on unit interval intersect at most three points?

Published on 13 Apr 2026 - 22:28

score 66 · Answer 11 · 2026-04-14 21:16:00

66

Views

Roots of an arc-length system

Published on 14 Apr 2026 - 21:16

score 58 · Answer 12 · 2026-04-14 18:01:05

58

Views

Number of polynomials with distinct roots.

Published on 14 Apr 2026 - 18:01

score 249 · Answer 13 · 2026-04-13 23:59:23

249

Views

Does $x^6 + x^2 + 1$ factor over an extension of $\mathbb{Z}$ by roots of unity?

Published on 13 Apr 2026 - 23:59

score 148 · Answer 14 · 2026-04-12 04:53:24

148

Views

Finding the roots of a polynomial to get expression for real part of a unit root of the heptadecagon

Published on 12 Apr 2026 - 4:53

score 39 · Answer 15 · 2026-04-16 08:17:18

39

Views

Solution of the functional equation $f\left( x,\, y \right)=x^{f(x,\,y-1)}\wedge\{x,\,y,\,f( x,\, y)\}\in\mathbb{C}$ and $x\ne0$

Published on 16 Apr 2026 - 8:17

List Question

Is this valid? $r_1^3+r_2^3+\cdots+r_7^3=(r_1+\cdots + r_7)^3-3(r_1+\cdots+r_7)(r_1r_2+r_1r_3+\cdots+r_6r_7)+3(r_1r_2r_3+r_1r_2r_4+\cdots+r_5r_6r_7)$

Poweriteration for polynomials with roots that have the same absolute value

Solution works for 2nd degree polynomial but does not extend to higher degrees.

Root representation using the factorization of polynomials upto degree six

Why isn't this root equation working out?

Do $p_n$ minus the number of integer solutions to this equation equal $(-1)^{\frac{1}{24} \left((p_n){}^2-1\right)}$ for $n>4$?

Complex argument in Chebyshev polynomials of second kind?

Finding fixed points of a specific constrained nonlinear PDE

Consider the curves $C_1: x^2y^2-a^2(x^2+y^2)=0, C_2: xy=a^2, C_3: x^2+y^2=a^2(a≠0).$ Count the number of points & tangents common to all three curves

Can these two concave functions on unit interval intersect at most three points?

Roots of an arc-length system

Number of polynomials with distinct roots.

Does $x^6 + x^2 + 1$ factor over an extension of $\mathbb{Z}$ by roots of unity?

Finding the roots of a polynomial to get expression for real part of a unit root of the heptadecagon

Solution of the functional equation $f\left( x,\, y \right)=x^{f(x,\,y-1)}\wedge\{x,\,y,\,f( x,\, y)\}\in\mathbb{C}$ and $x\ne0$

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