List questions from linear-diophantine-equations

60

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Let $a,b,c \in \mathbb{Z} \backslash \{ 0\}$. Prove there exists $x$, $y$ such that $ax+by=c$ if and only if $(a,b)|c$

Published on 24 Mar 2026 - 20:30

656

Views

Partition a list of positive and negative numbers into sets

Published on 24 Mar 2026 - 21:43

417

Views

How to show that $2x + 3y + 5z$ generate all integers greater than 2

Published on 25 Mar 2026 - 8:58

28

Views

Verification of Disproof of Linear Diophantine Equations

Published on 25 Mar 2026 - 3:35

243

Views

Diophantine equation

Published on 24 Mar 2026 - 16:14

85

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Positive diophantine solutions

Published on 24 Mar 2026 - 23:15

2.6k

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Diophantine equation with negative value

Published on 25 Mar 2026 - 8:32

62

Views

Almost diophantine equations?

Published on 24 Mar 2026 - 16:08

286

Views

Is there a shortcut for solving $ax-by=c$ when a,b,c are relatively prime?

Published on 18 Mar 2017 - 23:58

45

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Number of positive integer solutions of diophantine inequality.

Published on 01 Feb 2023 - 11:42

144

Views

Shortest palindromic Egyptian representation for reciprocal integers

Published on 23 Feb 2026 - 5:31

79

Views

$7x+5y=12$, so why does its solution will be of the format $(1+5n,1-7n)$

Published on 23 Feb 2026 - 12:05

121

Views

I am having difficulty understanding how to solve the diophantine equation $18x + 28y = 10$

Published on 26 Jun 2023 - 19:25

93

Views

Given a homogeneous system of Linear Equations mod $n$, if there are more equations than variables, can we tell if there exists a nontrivial solution?

Published on 25 Jul 2023 - 16:31

31

Views

Is this transformation of linear Diophanthine Equations always possible

Published on 28 Jul 2023 - 13:30

List Question

Let $a,b,c \in \mathbb{Z} \backslash \{ 0\}$. Prove there exists $x$, $y$ such that $ax+by=c$ if and only if $(a,b)|c$

Partition a list of positive and negative numbers into sets

How to show that $2x + 3y + 5z$ generate all integers greater than 2

Verification of Disproof of Linear Diophantine Equations

Diophantine equation

Positive diophantine solutions

Diophantine equation with negative value

Almost diophantine equations?

Is there a shortcut for solving $ax-by=c$ when a,b,c are relatively prime?

Number of positive integer solutions of diophantine inequality.

Shortest palindromic Egyptian representation for reciprocal integers

$7x+5y=12$, so why does its solution will be of the format $(1+5n,1-7n)$

I am having difficulty understanding how to solve the diophantine equation $18x + 28y = 10$

Given a homogeneous system of Linear Equations mod $n$, if there are more equations than variables, can we tell if there exists a nontrivial solution?

Is this transformation of linear Diophanthine Equations always possible

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