Fdtxjr

Is it inappropriate for a student to attend their mentor's dissertation defense?

Ambiguity in the definition of entropy

What mechanic is there to disable a threat instead of killing it?

Mathematica command that allows it to read my intentions

ssTTsSTtRrriinInnnnNNNIiinngg

Is it acceptable for a professor to tell male students to not think that they are smarter than female students?

What's the in-universe reasoning behind sorcerers needing material components?

Why didn't Boeing produce its own regional jet?

What killed these X2 caps?

How writing a dominant 7 sus4 chord in RNA ( Vsus7 chord in the 1st inversion)

All in one piece, we mend holes in your socks

Why is consensus so controversial in Britain?

One verb to replace 'be a member of' a club

What about the virus in 12 Monkeys?

How does a predictive coding aid in lossless compression?

How to Recreate this in LaTeX? (Unsure What the Notation is Called)

How did the Super Star Destroyer Executor get destroyed exactly?

How badly should I try to prevent a user from XSSing themselves?

Im going to France and my passport expires June 19th

How can I deal with my CEO asking me to hire someone with a higher salary than me, a co-founder?

Can we compute the area of a quadrilateral with one right angle when we only know the lengths of any three sides?

Is it logically or scientifically possible to artificially send energy to the body?

How can saying a song's name be a copyright violation?

What does the expression "A Mann!" means

Real Modulo Numbers in the Interval [0, 1), and Multiplication of

What are the rules for basic algebra when modulo real numbers are involvedDoes this number belong to the set of real numbers?What does the integer span of one irrational, and one (possibly irrational) real number look like in $mathbbR$?How to reverse modulo of a multiplication?Clarify a problem with prime and composite numbersDoes this prime generating way generate all the prime numbers?Why can we exchange numbers when working with modulo expressions?Does Arithmetic Need Non-Computable Real Numbers?Distribution of types of numbers in the real lineIs there any formal proof for the correctness of long multiplication/division method?

1

$begingroup$

Let's say we have a real number, A, in the interval [0, 1).
If we add another real number to it, it "Wraps" around back to zero.

So, for example:

Lets say: A = 5/13

If we multiply A by 2, we get: 10/13

If we multiple A by 3, we get: 2/13 (not 15/13)

If we multiple A by 4, we get 7/13 (not 20/13)

And so on...

My question is:

If given two such numbers, A and B, how can we find the smallest number, x, such that:

Ax = B

For example:

If A = 5/13 and B = 8/13, what do we need to multiply A by, to get B.

A solution for real numbers is preferable. However, if a solution does not exist for real numbers generally, then a solution for rational numbers should be sufficient.

Note that this problem is relevant to an algorithm that I'm writing. And I'd like to get it finished soon.

If I get my algorithm to work, and someone here provides a good solution, and that person (or people) have their name and contact details on their profile page, then I'm happy to give them a reference.

number-theory modular-arithmetic

share|cite|improve this question

edited Mar 21 at 20:34

Abs Spurdle

asked Mar 21 at 6:24

Abs SpurdleAbs Spurdle

113

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  My first thought would be to see if the (extended) Euclidean algorithm would be of any use: en.wikipedia.org/wiki/Modular_multiplicative_inverse
  $endgroup$
  – Matti P.
  Mar 21 at 6:29
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  For rational numbers $a/n$ and $b/n$, this is the same as solving the congruence $ax equiv b pmod n$. Solutions will not always exist (e.g., if $a = 2/4, b=1/4$).
  $endgroup$
  – FredH
  Mar 21 at 9:07
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I assumed that there was a solution with O(1), my bad. I had a look at the algorithm you suggested, and if I understand it correctly, it should work for the example above, however, it's not as efficient as I would like.
  $endgroup$
  – Abs Spurdle
  Mar 21 at 21:28
  

  
  
  
  

add a comment | 

1

$begingroup$

Let's say we have a real number, A, in the interval [0, 1).
If we add another real number to it, it "Wraps" around back to zero.

So, for example:

Lets say: A = 5/13

If we multiply A by 2, we get: 10/13

If we multiple A by 3, we get: 2/13 (not 15/13)

If we multiple A by 4, we get 7/13 (not 20/13)

And so on...

My question is:

If given two such numbers, A and B, how can we find the smallest number, x, such that:

Ax = B

For example:

If A = 5/13 and B = 8/13, what do we need to multiply A by, to get B.

A solution for real numbers is preferable. However, if a solution does not exist for real numbers generally, then a solution for rational numbers should be sufficient.

Note that this problem is relevant to an algorithm that I'm writing. And I'd like to get it finished soon.

If I get my algorithm to work, and someone here provides a good solution, and that person (or people) have their name and contact details on their profile page, then I'm happy to give them a reference.

number-theory modular-arithmetic

share|cite|improve this question

edited Mar 21 at 20:34

Abs Spurdle

asked Mar 21 at 6:24

Abs SpurdleAbs Spurdle

113

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  My first thought would be to see if the (extended) Euclidean algorithm would be of any use: en.wikipedia.org/wiki/Modular_multiplicative_inverse
  $endgroup$
  – Matti P.
  Mar 21 at 6:29
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  For rational numbers $a/n$ and $b/n$, this is the same as solving the congruence $ax equiv b pmod n$. Solutions will not always exist (e.g., if $a = 2/4, b=1/4$).
  $endgroup$
  – FredH
  Mar 21 at 9:07
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I assumed that there was a solution with O(1), my bad. I had a look at the algorithm you suggested, and if I understand it correctly, it should work for the example above, however, it's not as efficient as I would like.
  $endgroup$
  – Abs Spurdle
  Mar 21 at 21:28
  

  
  
  
  

add a comment | 

$begingroup$

Let's say we have a real number, A, in the interval [0, 1).
If we add another real number to it, it "Wraps" around back to zero.

So, for example:

Lets say: A = 5/13

If we multiply A by 2, we get: 10/13

If we multiple A by 3, we get: 2/13 (not 15/13)

If we multiple A by 4, we get 7/13 (not 20/13)

And so on...

My question is:

If given two such numbers, A and B, how can we find the smallest number, x, such that:

Ax = B

For example:

If A = 5/13 and B = 8/13, what do we need to multiply A by, to get B.

A solution for real numbers is preferable. However, if a solution does not exist for real numbers generally, then a solution for rational numbers should be sufficient.

Note that this problem is relevant to an algorithm that I'm writing. And I'd like to get it finished soon.

If I get my algorithm to work, and someone here provides a good solution, and that person (or people) have their name and contact details on their profile page, then I'm happy to give them a reference.

number-theory modular-arithmetic

share|cite|improve this question

edited Mar 21 at 20:34

Abs Spurdle

asked Mar 21 at 6:24

Abs SpurdleAbs Spurdle

113

$endgroup$

share|cite|improve this question

edited Mar 21 at 20:34

Abs Spurdle

asked Mar 21 at 6:24

Abs SpurdleAbs Spurdle

113

share|cite|improve this question

edited Mar 21 at 20:34

Abs Spurdle

asked Mar 21 at 6:24

Abs SpurdleAbs Spurdle

113

asked Mar 21 at 6:24

Abs SpurdleAbs Spurdle

113

asked Mar 21 at 6:24

Abs SpurdleAbs Spurdle

113