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Math Help - It is impossible to solve this basic prime numbers problem

  1. #1
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    It is impossible to solve this basic prime numbers problem

    given odd number e find prime p and q such that ((p-1)*(q-1)-1) is evenly divisible by e
    Last edited by rahulnaidu; May 6th 2010 at 06:09 PM.
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  2. #2
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    Quote Originally Posted by rahulnaidu View Post
    given prime number e find prime p and q such that ((p-1)*(q-1)-1) is evenly divisible by e
    Could this be worded better as e divides (p-1)(q-1)-1 such e,p,q \in P where P are prime numbers?
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  3. #3
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    sorry u could take that way
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  4. #4
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    I think it could be solved if some write a code for that, but if some one directly find those 2 numbers then the person math. genius
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  5. #5
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    2^n-1 generates prime numbers so we have.

    (2^n-1-1)(2^p-1-1)+1=(2^n-2)(2^p-2)-1=2^{n+p}-2^{p+1}-2^{n+1}+3<br />
    This what I have though of so far but don't have time to continue so what you can come up with.

    So we have e|2^{n+p}-2(2^{p}+2^{n}-1)+1. What do you mean be evenly divisible?
    Last edited by dwsmith; May 6th 2010 at 08:45 PM.
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  6. #6
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    am also trying for some time now couldn't figure it out.
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  7. #7
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    if it is divisible by 2 times,4times,6 times, like that
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  8. #8
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    Quote Originally Posted by rahulnaidu View Post
    given odd number e find prime p and q such that ((p-1)*(q-1)-1) is evenly divisible by e
    sorry i changed the problem it is odd number e not prime number e
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  9. #9
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    If e is odd, then e is of the form 2j+1.

    (2j+1)|2(2^{n+p-1}-2^{p}+2^{n}-1)+1. Now we have an odd number divides an odd number.

    Are we actually looking for numbers or just solving a general case?
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