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Finding a minimum $v$ given $N = d u + s v$, given positive integer $N, d, s$

Given a satisfactory real number = [any integer]/(2b) where a and b are integers, how would one find the minimum value of b?For any integer $a,b$ let $N_a,b$ denote the number of positive integer $x<1000$ satisfying $x= a( mod;27)$ and $x=b(mod;37)$. ThenHow do I prove that for every positive integer $n$, there exist $n$ consecutive positive integers, each of which is composite?Minimum difference between two AP termsFinding minimum difference between two linear functionsFinding smallest a+b from given condintions.Infinitely many positive integers of the form $1998k+1$ such that all digits in their decimal representation are equalNon-integer combinationGiven an integer $a$ how to find all integers $b$ such that $sqrta^2+b^2=k$ for some integer $k$?$a^2+b^2+c^2 = d^2+e^2+f^2 = m^2, ad + be = cf$ with $a,b,c,d,e,f$ all distinct positive integers

1

1

$begingroup$

We need to find a minimum of $v$ in :

$$N = du + sv$$

where $N, d,s$ are given positive integer, $u$ and $v$ are arbitrary positive integers.

For example, $19 = 5cdot 2 + 3cdot 3$ where $d,u,s,v = 5, 2, 3, 3$ resp.

How can we find a minimum of such a $v$, and if it may not exist?

I know very basic modulo properties, but they do not give direct answer.

algebra-precalculus elementary-number-theory

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edited Mar 28 at 16:55

jeea

60915

asked Mar 28 at 15:42

abcdeabcde

61

New contributor

abcde is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

1

1

$begingroup$

We need to find a minimum of $v$ in :

$$N = du + sv$$

where $N, d,s$ are given positive integer, $u$ and $v$ are arbitrary positive integers.

For example, $19 = 5cdot 2 + 3cdot 3$ where $d,u,s,v = 5, 2, 3, 3$ resp.

How can we find a minimum of such a $v$, and if it may not exist?

I know very basic modulo properties, but they do not give direct answer.

algebra-precalculus elementary-number-theory

share|cite|improve this question

edited Mar 28 at 16:55

jeea

60915

asked Mar 28 at 15:42

abcdeabcde

61

New contributor

abcde is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

$begingroup$

We need to find a minimum of $v$ in :

$$N = du + sv$$

where $N, d,s$ are given positive integer, $u$ and $v$ are arbitrary positive integers.

For example, $19 = 5cdot 2 + 3cdot 3$ where $d,u,s,v = 5, 2, 3, 3$ resp.

How can we find a minimum of such a $v$, and if it may not exist?

I know very basic modulo properties, but they do not give direct answer.

algebra-precalculus elementary-number-theory

share|cite|improve this question

edited Mar 28 at 16:55

jeea

60915

asked Mar 28 at 15:42

abcdeabcde

61

New contributor

abcde is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|cite|improve this question

edited Mar 28 at 16:55

jeea

60915

asked Mar 28 at 15:42

abcdeabcde

61

New contributor

abcde is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|cite|improve this question

edited Mar 28 at 16:55

jeea

60915

asked Mar 28 at 15:42

abcdeabcde

61

New contributor

abcde is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

edited Mar 28 at 16:55

jeea

60915

edited Mar 28 at 16:55

jeea

60915

asked Mar 28 at 15:42

abcdeabcde

61

New contributor

abcde is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked Mar 28 at 15:42

abcdeabcde

61