SOLUTION: If n = (p1 )^α1 .(p2)^α2.(p3)^α3 .(p4)^α4 .....(pr)^αr where p1 , p2, p3 , ...., pr are distinct prime numbers then prove the following result: d(n) = infinite product of

Algebra ->  Sequences-and-series -> SOLUTION: If n = (p1 )^α1 .(p2)^α2.(p3)^α3 .(p4)^α4 .....(pr)^αr where p1 , p2, p3 , ...., pr are distinct prime numbers then prove the following result: d(n) = infinite product of      Log On


   



Question 1172317: If n = (p1 )^α1 .(p2)^α2.(p3)^α3 .(p4)^α4 .....(pr)^αr where p1 , p2,
p3 , ...., pr are distinct prime numbers then prove the following result:
d(n) = infinite product of (αi + 1) [Note: Here ^ means power]

Answer by ikleyn(52782) About Me  (Show Source):
You can put this solution on YOUR website!
.

The post is written incorrectly.


Had the post be written correctly,  d(n)  would be a finite product, and  d(n)  would be called  (be referred)
as the number of divisors of the number  n, including 1 and the number n itself.


See the lesson
    - Problems on divisors of a given number
in this site.