How many divisors does a number have?

D

Darya

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How many divisors does "a" have if a, n are positive integer numbers?
[MATH]1)a=b^n[/MATH] b is a prime nymber
[MATH]2)2n=n^n[/MATH]
a)Claim 1 is sufficient by itself
b)Claim 2 is sufficient by itself
c)Both claims make sense only together, but none of them isn't sufficient by itself
d)None of them are sufficient

What's the logic in this question? I only got to the point that 'a' has n+1 devisors. Any hints? Thanks!
 
Are you trying to find [MATH]n[/MATH], or what? I don't completely understand the question.
 
Please check that you copied the problem exactly; if necessary, send us a picture of it. As written, it makes no sense.

I can see asking how many divisors [MATH]a[/MATH] has if [MATH]a[/MATH] is a power of a prime; but I don't see (1) as a "claim" about the number of divisors of an unknown number [MATH]a[/MATH].

And [MATH]2n = n^n[/MATH] is an equation with only a couple solutions, which has nothing to do with divisors.
 
I suggest that you try rewording your questions?

So does the first question mean

How many distinct positive integers divide evenly into b^n if b and n are both positive integers and b is a prime number?

If that is the question, then the answer is trivially n + 1. Presumably you meant something less obvious than that.
 
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