Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

henpen

  • 2 years ago

How many integer n exist so that \[ \frac{n}{100-n} \] is also an integer?

  • This Question is Closed
  1. henpen
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    What is the general strategy to be adopted for 'How many integer n exist so that f(n) is also an integer?', other than bursts of insight?

  2. RadEn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i think, trial error is the best way for this case

  3. sirm3d
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    suppose that for some integer k, \[k=\frac{ n }{ 100-n }\] rearranging the equation we get \[n=\frac{ 100k }{ k+1 }\] and since k and k+1 are relatively prime, we conclude that \[(k+1)|100\]

  4. henpen
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    What does the notation (k+1)|100 mean?

  5. sirm3d
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    (k+1) divides 100.

  6. sirm3d
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    when k = 0, n = 0. when k = 1, n = 50 when k = 3, n = 75

  7. sirm3d
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    there are more values for k, but the solution set is finite.

  8. henpen
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    OK, thanks or that

  9. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.