given odd number e find prime p and q such that ((p-1)*(q-1)-1) is evenly divisible by e

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- May 6th 2010, 04:32 PMrahulnaiduIt 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

- May 6th 2010, 04:35 PMdwsmith
- May 6th 2010, 04:38 PMrahulnaidu
sorry u could take that way

- May 6th 2010, 04:43 PMrahulnaidu
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

- May 6th 2010, 04:43 PMdwsmith
$\displaystyle 2^n-1 $generates prime numbers so we have.

$\displaystyle (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

$

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 $\displaystyle e|2^{n+p}-2(2^{p}+2^{n}-1)+1$. What do you mean be evenly divisible? - May 6th 2010, 04:45 PMrahulnaidu
am also trying for some time now couldn't figure it out.

- May 6th 2010, 05:08 PMrahulnaidu
if it is divisible by 2 times,4times,6 times, like that

- May 6th 2010, 05:10 PMrahulnaidu
- May 8th 2010, 08:52 AMdwsmith
If e is odd, then e is of the form $\displaystyle 2j+1$.

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

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