A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 4 years ago

The positive n integer is not divisible by 7 . The remainder when n is divided by 7 and the remainder when n^2 is divided by 7 are each equal to k . What is k? Help with solving a problem like this please!

  • This Question is Closed
  1. bahrom7893
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Let's try this the old fashioned long division way..

  2. bahrom7893
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1328418115277:dw|

  3. bahrom7893
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1328418167975:dw|

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

    |dw:1328418236084:dw|

  5. bahrom7893
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    sorry those are my random thoughts

  6. bahrom7893
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    don't have scrap paper on me

  7. bahrom7893
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    just gotta get the k in terms of n and 7.. hold on

  8. bahrom7893
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    im still thinkin btw haha

  9. bahrom7893
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    i think it's 1, just gotta prove it

  10. bahrom7893
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    okay, i think i got it: Suppose n=7a+k and n^2=7b+k

  11. bahrom7893
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    subtracting the two equations: n-n^2 = (7a+k) - (7b+k) or n-n^2 = 7a-7b = 7(a-b)

  12. bahrom7893
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    or n(n-1)=7(a-b). Now this means that either n is divisible by 7 or n-1 is divisible by 7.

  13. bahrom7893
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Let a-b be some integer, so n(n-1) = 7i. As I've said either n is divisible by 7 or n-1 is divisible by 7 (whichever one's divisible by 7 would mean that the other one's divisible by i).

  14. bahrom7893
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    We know that n is not divisible by 7 (given), that means n-1 must be divisible by 7

  15. bahrom7893
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Thus, if n-1 is some multiple of 7, n-1=7*x; or n = 7*x+1

  16. bahrom7893
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    which makes k = 1. Actually let's test this.

  17. bahrom7893
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    8/7 has remainder 1, so does 64/7

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

    Try 30 and then 30^2 and test for equal remainders.

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

    Use congruences k=1

  20. jhonyy9
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    n : 7 =x+k n^2 :7=y+k k=? n :7 =x+k --- n=x*7 +k ((x*7)+k)^2 :7=y+k 49x^2 +14kx +k^2 =7y+7k 14kx +k^2 -7k =7y-49x^2 k^2 +7k(2x-1) =7y-49x^2 k^2 +7(2x-1)k -7y+49x^2 =0 k^2 +7(2x-1)k -7(y-7x^2) =0 --- so now just you need to solve this quadratic equation for k_1 and k_2 .... - hope that is understandably !!! good luck bye

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

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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.