Let n = 2^31 3^19. How many positive divisors of n^2 are less than n but

do not divide n?

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- Jan 14th 2011, 02:45 AMrcspositive divisor
Let n = 2^31 3^19. How many positive divisors of n^2 are less than n but

do not divide n? - Jan 14th 2011, 02:57 AMtonio
- Jan 14th 2011, 08:04 AMOpalg
A divisor of must be of the form , with and . If it does not divide then

__either____or__.

Now comes the tricky part. The remaining condition is that . I suggest that you investigate this by choosing a random value of p between 31 and 62, say p=45, and looking at how many values of q satisfy the condition . [Hint: take logs.] That may possibly give you some insight into how to tackle the problem in general. - Jan 15th 2011, 12:50 AMrcs
it is said that the answer is 589 but i dont know how it is reached to this.

- Jan 15th 2011, 02:35 AMemakarov
This question has already been discussed, but I have not tried to find a more elegant solution.