(A) Determine the total number of ways in which 10²⁰¹⁰(base ten) is expressible as the product of:

(I) Four distinct positive integers arranged in increasing order of magnitude.

(II) Five distinct positive integers arranged in increasing order of magnitude.

(III) Six distinct positive integers arranged in increasing order of magnitude.

(B) What are the respective answers to each of (I), (II) and (III) in part-(A), if 10²⁰¹⁰(base ten) is replaced by 10²⁰¹⁰(base 12)?

(In reply to re(2): Initial thoughts. by Jer)

I agree it doesn't keep the numbers distinct. I was really thinking more in the context of the current problem which is a power of a composite number, where the other prime's power would supply the distinctness, and falsely attributed this to an equivalent prime power problem.

Posted by Charlie on 2011-03-21 16:07:35