Question

Prove that if a sequence with $50$ members is $p$-balanced for $p=3,5,7,11,13, 17$, then all its members are equal zero.

score 171 · Answer 1 · 2015-10-23 04:59:03

171

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Prove that if a sequence with $50$ members is $p$-balanced for $p=3,5,7,11,13, 17$, then all its members are equal zero.

Published on 23 Oct 2015 - 4:59

score 46 · Answer 2 · 2026-04-02 09:34:15

46

Views

Suppose $X\sim\mathrm{Poisson} (N)$ where $N\sim\mathrm{Poisson}(\lambda)$, What is the P.G.F of $X+N$?

Published on 02 Apr 2026 - 9:34

score 97 · Answer 3 · 2026-04-04 07:27:15

97

Views

Can one do anything useful with a functional equation like $g(x^2) = \frac{4x^2-1}{2x^2+1}g(x)$?

Published on 04 Apr 2026 - 7:27

score 805 · Answer 4 · 2015-10-27 01:40:22

805

Views

Leningrad Mathematical Olympiad $1991$

Published on 27 Oct 2015 - 1:40

score 136 · Answer 5 · 2015-10-28 09:20:48

136

Views

Solution to closed form of a Generating function

Published on 28 Oct 2015 - 9:20

score 176 · Answer 6 · 2015-10-28 13:53:18

176

Views

Generating function of Catalan numbers.

Published on 28 Oct 2015 - 13:53

score 453 · Answer 7 · 2015-10-30 20:14:44

453

Views

Generating function of (-3)^n

Published on 30 Oct 2015 - 20:14

score 189 · Answer 8 · 2026-03-29 10:46:52

189

Views

2-dimensional moment generating function of (X, logX)

Published on 29 Mar 2026 - 10:46

score 770 · Answer 9 · 2015-11-02 00:39:29

770

Views

Closed Form Generating Function for sum of natural numbers

Published on 02 Nov 2015 - 0:39

score 172 · Answer 10 · 2015-11-02 09:01:14

172

Views

How to find the sum $\sum_{i = 0}^{\infty}\frac{F_i}{7^i}$?

Published on 02 Nov 2015 - 9:01

score 79 · Answer 11 · 2015-11-04 11:55:39

79

Views

If $G(s)=G(p+qs)e^{\lambda(s-1)}$ then $G(s)=e^{\lambda(s-1)/p}$

Published on 04 Nov 2015 - 11:55

score 453 · Answer 12 · 2026-03-31 08:06:06

453

Views

Generating function of Riemann zeta function

Published on 31 Mar 2026 - 8:06

score 285 · Answer 13 · 2015-11-05 18:04:04

285

Views

$n$-words over the alphabet $\{0,...,d\}$ without consecutive $0$'s

Published on 05 Nov 2015 - 18:04

score 180 · Answer 14 · 2015-11-05 22:58:11

180

Views

Find the coefficient of $x^n$ in $\sqrt{1 - 8x}$.

Published on 05 Nov 2015 - 22:58

score 99 · Answer 15 · 2015-11-06 01:51:02

99

Views

Expression for recurrence relation $a_n$ using exponential generating functions

Published on 06 Nov 2015 - 1:51

List Question

Prove that if a sequence with $50$ members is $p$-balanced for $p=3,5,7,11,13, 17$, then all its members are equal zero.

Suppose $X\sim\mathrm{Poisson} (N)$ where $N\sim\mathrm{Poisson}(\lambda)$, What is the P.G.F of $X+N$?

Can one do anything useful with a functional equation like $g(x^2) = \frac{4x^2-1}{2x^2+1}g(x)$?

Leningrad Mathematical Olympiad $1991$

Solution to closed form of a Generating function

Generating function of Catalan numbers.

Generating function of (-3)^n

2-dimensional moment generating function of (X, logX)

Closed Form Generating Function for sum of natural numbers

How to find the sum $\sum_{i = 0}^{\infty}\frac{F_i}{7^i}$?

If $G(s)=G(p+qs)e^{\lambda(s-1)}$ then $G(s)=e^{\lambda(s-1)/p}$

Generating function of Riemann zeta function

$n$-words over the alphabet $\{0,...,d\}$ without consecutive $0$'s

Find the coefficient of $x^n$ in $\sqrt{1 - 8x}$.

Expression for recurrence relation $a_n$ using exponential generating functions

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