Question

Give the complete factorization of $P_n(X)=\frac{(X+i)^{2n+1} - (X-i)^{2n+1}}{2i} = 0$

score 39 · Answer 1 · 2026-04-17 09:05:24

39

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Give the complete factorization of $P_n(X)=\frac{(X+i)^{2n+1} - (X-i)^{2n+1}}{2i} = 0$

Published on 17 Apr 2026 - 9:05

score 82 · Answer 2 · 2026-04-12 22:25:30

82

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Factoring a quadratic mod $p$

Published on 12 Apr 2026 - 22:25

score 151 · Answer 3 · 2026-04-09 04:06:55

151

Views

How to find the numbers efficiently given their sum and product?

Published on 09 Apr 2026 - 4:06

score 58 · Answer 4 · 2026-04-15 22:13:10

58

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How to obtain the complete factorization of $P_n(X)=\frac{(X+i)^{2n+1} - (X-i)^{2n+1}}{2i} = 0$

Published on 15 Apr 2026 - 22:13

score 113 · Answer 5 · 2026-04-15 16:17:20

113

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A question related to $f(n)=n^4+n^2+1$

Published on 15 Apr 2026 - 16:17

score 76 · Answer 6 · 2026-04-17 00:49:21

76

Views

Suppose $\gcd(a,b,c)=1$. Then is $a^n+b^n+c^n$ divisible by $a+b+c$?

Published on 17 Apr 2026 - 0:49

score 197 · Answer 7 · 2026-04-12 19:08:51

197

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According to what rigorous definition of "polynomial" is $\sum_{k=0}^n a_k D^k$ a polynomial, where $D$ is the derivative operator?

Published on 12 Apr 2026 - 19:08

score 51 · Answer 8 · 2026-04-16 01:02:28

51

Views

Write $x$ in terms of $y$ in inequality ${x}^{2}+x\le y$

Published on 16 Apr 2026 - 1:02

score 55 · Answer 9 · 2026-04-17 11:24:08

How did this binomial $(x^2+3)^{-\frac 13}-\frac 23x^2(x^2+3)^{-\frac 43}$ get factored into these $(x^2+3)^{-\frac 43}(\frac 13x^2+3)$ factors?

score 28 · Answer 10 · 2026-04-12 01:37:01

28

Views

Do iterated quadratic polynomials have the minimal number of irreducible factors?

Published on 12 Apr 2026 - 1:37

score 440 · Answer 11 · 2026-04-16 12:00:55

440

Views

Find the number of positive divisors of $(2008^3 + (3 * 2008 * 2009) + 1)^2$

Published on 16 Apr 2026 - 12:00

score 135 · Answer 12 · 2026-04-13 20:17:12

135

Views

Collatz conjecture: What if we prove $3x+1$ cycles factors?

Published on 13 Apr 2026 - 20:17

score 502 · Answer 13 · 2026-04-18 01:30:36

502

Views

Deriving kinetic energy from Newton's Second Law (step I don't understand)

Published on 18 Apr 2026 - 1:30

score 646 · Answer 14 · 2026-04-12 22:30:14

646

Views

Find the highest natural number which is divisible by $30$ and has exactly $30$ different positive divisors.

Published on 12 Apr 2026 - 22:30

score 113 · Answer 15 · 2026-04-12 09:50:16

113

Views

Does being able to factor semiprimes entail being able to factor any number?

Published on 12 Apr 2026 - 9:50

List Question

Give the complete factorization of $P_n(X)=\frac{(X+i)^{2n+1} - (X-i)^{2n+1}}{2i} = 0$

Factoring a quadratic mod $p$

How to find the numbers efficiently given their sum and product?

How to obtain the complete factorization of $P_n(X)=\frac{(X+i)^{2n+1} - (X-i)^{2n+1}}{2i} = 0$

A question related to $f(n)=n^4+n^2+1$

Suppose $\gcd(a,b,c)=1$. Then is $a^n+b^n+c^n$ divisible by $a+b+c$?

According to what rigorous definition of "polynomial" is $\sum_{k=0}^n a_k D^k$ a polynomial, where $D$ is the derivative operator?

Write $x$ in terms of $y$ in inequality ${x}^{2}+x\le y$

How did this binomial $(x^2+3)^{-\frac 13}-\frac 23x^2(x^2+3)^{-\frac 43}$ get factored into these $(x^2+3)^{-\frac 43}(\frac 13x^2+3)$ factors?

Do iterated quadratic polynomials have the minimal number of irreducible factors?

Find the number of positive divisors of $(2008^3 + (3 * 2008 * 2009) + 1)^2$

Collatz conjecture: What if we prove $3x+1$ cycles factors?

Deriving kinetic energy from Newton's Second Law (step I don't understand)

Find the highest natural number which is divisible by $30$ and has exactly $30$ different positive divisors.

Does being able to factor semiprimes entail being able to factor any number?

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