Question

Prove that $yx = qxy$ implies $(x + y)^d = x^d + y^d.$

score 164 · Answer 1 · 2026-04-17 06:18:38

164

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Prove that $yx = qxy$ implies $(x + y)^d = x^d + y^d.$

Published on 17 Apr 2026 - 6:18

score 140 · Answer 2 · 2026-04-09 03:20:51

140

Views

Understanding iterative method to calculate binomial coefficients for distribution

Published on 09 Apr 2026 - 3:20

score 49 · Answer 3 · 2026-04-11 19:25:11

49

Views

big O growth function of binomial coefficient C(r,k) in Concrete Mathematics book on page 163

Published on 11 Apr 2026 - 19:25

score 48 · Answer 4 · 2026-04-15 06:29:54

48

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Find the value of r in the largest term in $(5+2x)^{14}$ where $T(r)$ is the $r$-th term and $x=4/3$

Published on 15 Apr 2026 - 6:29

score 121 · Answer 5 · 2026-04-15 03:36:25

121

Views

Using group theory, show that $\forall \ n\in \mathbb Z_{\geq 0}, \ (n+1)$ divides ${2n}\choose{n}$

Published on 15 Apr 2026 - 3:36

score 155 · Answer 6 · 2026-04-16 05:32:35

155

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Prove $\sum_{k=1}^{n}k^2\binom{n+k}{k}=\frac{n(n+1)^3\binom{2n+1}{n+1}}{(n+2)(n+3)}$

Published on 16 Apr 2026 - 5:32

score 164 · Answer 7 · 2026-04-15 18:08:40

164

Views

Combinatorial proof $\binom{2n}{3} = 2 \binom{n}{3} + 2n \binom{n}{2}$

Published on 15 Apr 2026 - 18:08

score 241 · Answer 8 · 2026-04-10 14:55:46

241

Views

Strange binomial sum

Published on 10 Apr 2026 - 14:55

score 73 · Answer 9 · 2026-04-14 00:30:03

73

Views

Trying to show that $\binom{2m}{m} \leq 2^{2m} \frac{2m-1}{6m}$

Published on 14 Apr 2026 - 0:30

score 482 · Answer 10 · 2026-03-25 20:53:32

482

Views

Trick for calculating the 5th order derivative of $(2x^3+1)e^{x^2}$ evaluated at $0$

Published on 25 Mar 2026 - 20:53

score 67 · Answer 11 · 2026-04-14 15:15:46

67

Views

Expectation of a certain polynomial expression in Rademacher random variables.

Published on 14 Apr 2026 - 15:15

score 139 · Answer 12 · 2026-04-14 19:52:40

139

Views

How can I prove this formula: $\sum_{a_1+a_2+\cdots +a_m\le n}\prod_{i=1}^ma_i=\binom{n+m}{2m}$?

Published on 14 Apr 2026 - 19:52

score 80 · Answer 13 · 2026-04-13 16:05:49

80

Views

What are the Binomial Theorem and General Leibniz rule special cases of?

Published on 13 Apr 2026 - 16:05

score 60 · Answer 14 · 2026-04-14 17:54:40

60

Views

evidence Z for a binomial distribution as a beta distribution is uniform on discrete support interval

Published on 14 Apr 2026 - 17:54

score 34 · Answer 15 · 2026-03-25 09:43:07

34

Views

How does Ireland-Rosen reduce the coefficient of $z^{\frac{p-1}{2}}$ into this neat form in Kronecker proof of Gaussian sums?

Published on 25 Mar 2026 - 9:43

List Question

Prove that $yx = qxy$ implies $(x + y)^d = x^d + y^d.$

Understanding iterative method to calculate binomial coefficients for distribution

big O growth function of binomial coefficient C(r,k) in Concrete Mathematics book on page 163

Find the value of r in the largest term in $(5+2x)^{14}$ where $T(r)$ is the $r$-th term and $x=4/3$

Using group theory, show that $\forall \ n\in \mathbb Z_{\geq 0}, \ (n+1)$ divides ${2n}\choose{n}$

Prove $\sum_{k=1}^{n}k^2\binom{n+k}{k}=\frac{n(n+1)^3\binom{2n+1}{n+1}}{(n+2)(n+3)}$

Combinatorial proof $\binom{2n}{3} = 2 \binom{n}{3} + 2n \binom{n}{2}$

Strange binomial sum

Trying to show that $\binom{2m}{m} \leq 2^{2m} \frac{2m-1}{6m}$

Trick for calculating the 5th order derivative of $(2x^3+1)e^{x^2}$ evaluated at $0$

Expectation of a certain polynomial expression in Rademacher random variables.

How can I prove this formula: $\sum_{a_1+a_2+\cdots +a_m\le n}\prod_{i=1}^ma_i=\binom{n+m}{2m}$?

What are the Binomial Theorem and General Leibniz rule special cases of?

evidence Z for a binomial distribution as a beta distribution is uniform on discrete support interval

How does Ireland-Rosen reduce the coefficient of $z^{\frac{p-1}{2}}$ into this neat form in Kronecker proof of Gaussian sums?

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