Question

How to show that $\gcd(a_1,a_2,\cdots,a_k) = 1$ implies that there exist a non-negative solution to $\sum_{i=1}^{n}a_ix_i = n$ for large $n.$

score 426 · Answer 1 · 2026-03-25 08:58:54

426

Views

How to show that $\gcd(a_1,a_2,\cdots,a_k) = 1$ implies that there exist a non-negative solution to $\sum_{i=1}^{n}a_ix_i = n$ for large $n.$

Published on 25 Mar 2026 - 8:58

score 720 · Answer 2 · 2026-03-27 05:37:53

720

Views

Laplace transform of "shifted" modified Bessel function

Published on 27 Mar 2026 - 5:37

score 103 · Answer 3 · 2019-01-04 13:17:41

103

Views

generating function of numbers of visits up to time n

Published on 04 Jan 2019 - 13:17

score 808 · Answer 4 · 2019-01-04 17:21:25

808

Views

Find the probability generating function of $Z=\sum_{i=1}^{N}X_i.$

Published on 04 Jan 2019 - 17:21

score 115 · Answer 5 · 2026-03-25 11:13:34

115

Views

which one is worse in terms of probability

Published on 25 Mar 2026 - 11:13

score 49 · Answer 6 · 2026-03-25 06:03:49

49

Views

Shifting roots in infinite sums of polynomials

Published on 25 Mar 2026 - 6:03

score 463 · Answer 7 · 2019-01-07 08:31:36

463

Views

Is there a function for mapping 1 to 1, 2 to 2...n to n, 1,2 to n+1, 1,3 to n+2...1,n-1 to 2n-1 for n variables?

Published on 07 Jan 2019 - 8:31

score 59 · Answer 8 · 2026-03-26 04:49:24

59

Views

Does this bivariate function have a non-summation form or a good looking generating function?

Published on 26 Mar 2026 - 4:49

score 82 · Answer 9 · 2026-03-26 08:03:52

82

Views

Generating function for Fibonacci-like sequence

Published on 26 Mar 2026 - 8:03

score 110 · Answer 10 · 2019-01-08 23:22:47

110

Views

Recurrence relations in Matrices raised to natural powers

Published on 08 Jan 2019 - 23:22

score 98 · Answer 11 · 2026-03-25 23:38:11

98

Views

Find the distribution of $Z=X+Y$ where both $X$ and $Y$ are exponentially distributed.

Published on 25 Mar 2026 - 23:38

score 192 · Answer 12 · 2026-03-25 07:31:11

192

Views

Convergence of Exponential Generating Functions

Published on 25 Mar 2026 - 7:31

score 86 · Answer 13 · 2019-01-14 03:16:07

86

Views

Is there some way to prove $n\binom nr=(r+1)\binom n{r+1}+r\binom nr$ using generating functions?

Published on 14 Jan 2019 - 3:16

score 439 · Answer 14 · 2019-01-14 05:51:25

Calculating and proving the generating function for the recursion $a_n = 2a_{n-1} + a_{n-2}$ with $a_0 = 1$ and $a_1 = 3$?

score 107 · Answer 15 · 2019-01-14 07:31:12

107

Views

Finding the explicit formula for the recursion $a_n = 2a_{n-1} + a_{n-2}$ with $a_0 = 1$ and $a_1 = 3$?

Published on 14 Jan 2019 - 7:31

List Question

How to show that $\gcd(a_1,a_2,\cdots,a_k) = 1$ implies that there exist a non-negative solution to $\sum_{i=1}^{n}a_ix_i = n$ for large $n.$

Laplace transform of "shifted" modified Bessel function

generating function of numbers of visits up to time n

Find the probability generating function of $Z=\sum_{i=1}^{N}X_i.$

which one is worse in terms of probability

Shifting roots in infinite sums of polynomials

Is there a function for mapping 1 to 1, 2 to 2...n to n, 1,2 to n+1, 1,3 to n+2...1,n-1 to 2n-1 for n variables?

Does this bivariate function have a non-summation form or a good looking generating function?

Generating function for Fibonacci-like sequence

Recurrence relations in Matrices raised to natural powers

Find the distribution of $Z=X+Y$ where both $X$ and $Y$ are exponentially distributed.

Convergence of Exponential Generating Functions

Is there some way to prove $n\binom nr=(r+1)\binom n{r+1}+r\binom nr$ using generating functions?

Calculating and proving the generating function for the recursion $a_n = 2a_{n-1} + a_{n-2}$ with $a_0 = 1$ and $a_1 = 3$?

Finding the explicit formula for the recursion $a_n = 2a_{n-1} + a_{n-2}$ with $a_0 = 1$ and $a_1 = 3$?

Trending Questions

Popular # Hahtags

Popular Questions