Question

Is there an algorithm to simplify solutions of linear Diophantine Equations?

score 92 · Answer 1 · 2022-05-25 22:17:28

92

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Is there an algorithm to simplify solutions of linear Diophantine Equations?

Published on 25 May 2022 - 22:17

score 309 · Answer 2 · 2022-05-27 00:41:22

309

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Let p be a prime. Prove that $x^4 + 4 y^4 = p$ has integer solutions if and only if $p = 5$. In this case, find the solutions for x and y.

Published on 27 May 2022 - 0:41

score 50 · Answer 3 · 2022-06-02 21:58:00

50

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Can $c^2(a\cdot b)+c(a+b)=2^c-2$ be solved to find $\mathbb{N}$ solutions?

Published on 02 Jun 2022 - 21:58

score 26 · Answer 4 · 2022-06-11 13:04:55

26

Views

Solving $c = ab$ in $(\mathbb{Z}_n,+)$

Published on 11 Jun 2022 - 13:04

score 109 · Answer 5 · 2022-06-11 17:19:10

109

Views

Given $n$ integers $a_1$ to $a_n$ and an integer $K$, does there exist a solution which satisfies the following equation?

Published on 11 Jun 2022 - 17:19

score 56 · Answer 6 · 2022-06-25 08:20:43

56

Views

Consecutive integers 8p, 9q, 10r: search for small solution sets (p,q,r) other than (1,1,1).

Published on 25 Jun 2022 - 8:20

score 54 · Answer 7 · 2022-06-29 15:43:10

54

Views

Finding the biggest $k\leq k_0$ such that the interval $k[A, B]$ contains an integer

Published on 29 Jun 2022 - 15:43

score 81 · Answer 8 · 2022-09-29 13:50:19

81

Views

What is the complexity of solving this specific System of Diophantine Equations?

Published on 29 Sep 2022 - 13:50

score 44 · Answer 9 · 2022-11-05 12:08:07

44

Views

minimum solutions for linear Diophantine equation in n variables

Published on 05 Nov 2022 - 12:08

score 159 · Answer 10 · 2022-11-12 02:11:38

159

Views

Is there a way to find the values of 3 variables with just one equation?

Published on 12 Nov 2022 - 2:11

score 255 · Answer 11 · 2022-11-29 09:32:21

255

Views

How many solutions to this Diophantine equation group of Com Quantum Theory? Does it have a general solution method?

Published on 29 Nov 2022 - 9:32

score 20 · Answer 12 · 2022-12-07 08:11:37

20

Views

Bound on minimimal non-negative linear diophantine equation in two variables

Published on 07 Dec 2022 - 8:11

score 40 · Answer 13 · 2022-12-14 17:56:04

40

Views

Given two positive integers a , b , $gcd(a, b) = 1$, prove for any integer n > ab-a-b there exist integers $x, y\ge0$ such that $ax+by = n$

Published on 14 Dec 2022 - 17:56

score 54 · Answer 14 · 2023-01-17 11:17:37

54

Views

Are the solution sets equal for diophantine equation with opposite general solution signs at parameter?

Published on 17 Jan 2023 - 11:17

score 238 · Answer 15 · 2023-01-26 01:58:02

238

Views

How many different sets of positive integers $(a, b, c, d)$ are there such that $a \lt b \lt c \lt d$ and $a + b + c + d = 41$?

Published on 26 Jan 2023 - 1:58

List Question

Is there an algorithm to simplify solutions of linear Diophantine Equations?

Let p be a prime. Prove that $x^4 + 4 y^4 = p$ has integer solutions if and only if $p = 5$. In this case, find the solutions for x and y.

Can $c^2(a\cdot b)+c(a+b)=2^c-2$ be solved to find $\mathbb{N}$ solutions?

Solving $c = ab$ in $(\mathbb{Z}_n,+)$

Given $n$ integers $a_1$ to $a_n$ and an integer $K$, does there exist a solution which satisfies the following equation?

Consecutive integers 8p, 9q, 10r: search for small solution sets (p,q,r) other than (1,1,1).

Finding the biggest $k\leq k_0$ such that the interval $k[A, B]$ contains an integer

What is the complexity of solving this specific System of Diophantine Equations?

minimum solutions for linear Diophantine equation in n variables

Is there a way to find the values of 3 variables with just one equation?

How many solutions to this Diophantine equation group of Com Quantum Theory? Does it have a general solution method?

Bound on minimimal non-negative linear diophantine equation in two variables

Given two positive integers a , b , $gcd(a, b) = 1$, prove for any integer n > ab-a-b there exist integers $x, y\ge0$ such that $ax+by = n$

Are the solution sets equal for diophantine equation with opposite general solution signs at parameter?

How many different sets of positive integers $(a, b, c, d)$ are there such that $a \lt b \lt c \lt d$ and $a + b + c + d = 41$?

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