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King

  • 3 years ago

:Help...........for how many positive integers n is n^3 -8n^2+20n-13 a prime number??

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  1. sheg
    • 3 years ago
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    factorize it

  2. King
    • 3 years ago
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    how watever i get is not a prime number

  3. King
    • 3 years ago
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    why?

  4. King
    • 3 years ago
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    oh

  5. King
    • 3 years ago
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    but then ii have to plug in millions of values

  6. sheg
    • 3 years ago
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    what u want to calculate

  7. sheg
    • 3 years ago
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    (n^3 -8n^2+20n-13) a prime number

  8. sheg
    • 3 years ago
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    or n is a prime number

  9. King
    • 3 years ago
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    for n i will have to put millions of values to find how may n positive integers satisfy n^3 -8n^2+20n-13 to be a prime number

  10. sheg
    • 3 years ago
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    ok

  11. King
    • 3 years ago
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    so,what to do??

  12. King
    • 3 years ago
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    anything i can do to narrow down the possobilities

  13. King
    • 3 years ago
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    no answer given....

  14. sheg
    • 3 years ago
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    ok see for 2 it is prime number

  15. sheg
    • 3 years ago
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    wait i took wrong concept

  16. sheg
    • 3 years ago
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    \[(x-1) \times [(x-7)x + 13]\]

  17. sheg
    • 3 years ago
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    where x is n

  18. King
    • 3 years ago
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    ok

  19. sheg
    • 3 years ago
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    now see the first term is (x-1). and other than 2 no other even number is a prime number right

  20. sheg
    • 3 years ago
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    i got the answer

  21. King
    • 3 years ago
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    no n does not have to be a prime number n^3 -8n^2+20n-13 has to be a prime number

  22. sheg
    • 3 years ago
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    yeah i know (x−1)×[(x−7)x+13] it has to be prime

  23. King
    • 3 years ago
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    yup so x can be anything greater or equal to 2

  24. sheg
    • 3 years ago
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    first term is (x-1) and two is the only even prime number.

  25. sheg
    • 3 years ago
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    but if u will subtract 1 from any other prime number the resultant will be divisible by 2

  26. sheg
    • 3 years ago
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    getting my point or not

  27. King
    • 3 years ago
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    x can be 4

  28. sheg
    • 3 years ago
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    yeah u r right

  29. sheg
    • 3 years ago
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    it means that for any odd integer other than 3 u will not get a prime number

  30. King
    • 3 years ago
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    yeah

  31. FoolForMath
    • 3 years ago
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    Superb sheggy!

  32. sheg
    • 3 years ago
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    also the number cannot be graeter than 7

  33. King
    • 3 years ago
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    oh yeah

  34. sheg
    • 3 years ago
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    thanks fool bhai

  35. sheg
    • 3 years ago
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    so u are having a limited space to work out that is from 1 to 7

  36. King
    • 3 years ago
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    yes sheg u got it so answer is n=2,3,4

  37. King
    • 3 years ago
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    no actually 2 to 7

  38. sheg
    • 3 years ago
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    hahahaa right 2 to 7

  39. sheg
    • 3 years ago
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    but for 7 it will be 0

  40. King
    • 3 years ago
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    wait why cant it be greater than 7?

  41. sheg
    • 3 years ago
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    try any number u will get the answer

  42. sheg
    • 3 years ago
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    odd numbers cannot be included ok thats true

  43. sheg
    • 3 years ago
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    as i had told u any odd number subtracted by one will result in even number so it will be divisible by 2.........do u accept it or not

  44. King
    • 3 years ago
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    is 323 a prime number?

  45. King
    • 3 years ago
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    yeah i acept

  46. King
    • 3 years ago
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    its not div by 17

  47. sheg
    • 3 years ago
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    323 is divisible by 17

  48. sheg
    • 3 years ago
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    so 323 is not a prime number

  49. King
    • 3 years ago
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    4387 ?

  50. sheg
    • 3 years ago
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    what u have put x = ??

  51. King
    • 3 years ago
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    n=20

  52. King
    • 3 years ago
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    1443?

  53. King
    • 3 years ago
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    gtg shall come bak in 15 min

  54. sheg
    • 3 years ago
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    for n = 20 it should be equal to 5187

  55. King
    • 3 years ago
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    oh yeah 1443?

  56. King
    • 3 years ago
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    no

  57. sheg
    • 3 years ago
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    20^3 - 8*20^2 + 20*20 -13 =8000 - 3200 + 400 -13 = 8400 - 3213 = 5187

  58. King
    • 3 years ago
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    gtg cum bak in 15 mins

  59. sheg
    • 3 years ago
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    dear i had told u for no value greater than 7 it would fit

  60. sheg
    • 3 years ago
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    and both 1443 and 5187 is divisible by 3

  61. King
    • 3 years ago
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    i am bak so what to do now?

  62. sheg
    • 3 years ago
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    for no value greater than 7 that too even number it will not be a prime number

  63. sheg
    • 3 years ago
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    http://www.wolframalpha.com/input/?i=x^3-8x^2%2B20x-13+where+x+%3D+20 visit this website and plug in different value of x u will get the answer

  64. sheg
    • 3 years ago
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    king u there

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