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jhonyy9

  • 4 years ago

- for example : (2-1) (2-1) ----- + ------ +1 = 2 2 2 (3-1) (3-1) ----- + ----- +1 =3 2 2 (5-1) (3-1) ----- + ----- +1 = 2 +1 +1 =4 2 2 (5-1) (5-1) ----- + ----- +1 = 2+2+1=5 2 2 can be this proven that is true for every natural numbers ?

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  1. jhonyy9
    • 4 years ago
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    can be do it by induction ?

  2. EscherichiaRinku
    • 4 years ago
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    The difficult part here is probably getting a general formula. Then proving it by induction shouldn't be hard.

  3. hoblos
    • 4 years ago
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    (a-1) (a-1) 2a -2 ----- + ------ +1 = ------- +1 = a-1+1 =a 2 2 2

  4. hoblos
    • 4 years ago
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    this is true for any natural number

  5. jhonyy9
    • 4 years ago
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    ,,hoblos" yes i see it but this need to be proven

  6. jhonyy9
    • 4 years ago
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    -so if we know that p and k are primes

  7. jhonyy9
    • 4 years ago
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    - prove that for every n natural numbers grater or equal 2 exist one p and k numbers prim grater or equal 2 such that the below equation is true : (p-1) (k-1) ----- + ----- +1 = n 2 2

  8. jhonyy9
    • 4 years ago
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    this was my previosly question

  9. jhonyy9
    • 4 years ago
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    so than p=2a+1 and k=2b+1

  10. hoblos
    • 4 years ago
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    actually there exist more than one p & k such that the equation is true!! for example: if n=4 you may take (p=5 k=3) or (p=7 k=1) but there is one condition that must be satisfied which is n=(p+k)/2

  11. jhonyy9
    • 4 years ago
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    so but do you can prove it in one proning style ,method that is true for every natural numbers ?

  12. jhonyy9
    • 4 years ago
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    sorry proving stayle ,method

  13. jhonyy9
    • 4 years ago
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    style ,method

  14. hoblos
    • 4 years ago
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    well.. i have only this method for now for all natural numbers p & k , there exist n such that (p-1) (k-1) ----- + ----- +1 = n => (p+k)/2 -1+1=n => n=(p+k)/2 2 2

  15. jhonyy9
    • 4 years ago
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    not right because if you see the first sentence of this exercise there is that p and k are prims

  16. hoblos
    • 4 years ago
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    they dont have to be primes try p=6 k=4 and you will get n=5 the exercise is also stating that we have only one p&k while we have more than one!!

  17. jhonyy9
    • 4 years ago
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    but is indifferent from this exercise p and k are prims

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