Product of divisors number theory problem

  • Thread starter lei123
  • Start date
  • #1
11
0

Homework Statement


prove using induction:
for any n =1,2,3...
the product of the divisors of n = n^(number of divisors of n (counting 1 and n)/2)


Homework Equations





The Attempt at a Solution


I understand why this is the case, but I'm having trouble with the induction step.
if the product of the divisors of k = k^(number of divisors of k/2), the the product of the divisors of k+1 = k^(number of divisors of k+1/2). I know that k and k+1 are relatively prime, so all their divisors are different. But I can't seem to make that final connection
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
251
hi lei123! :smile:

i've no idea why anyone would want to prove it by induction :confused:

but if you do, then as you say, using induction on the number n itself won't work, so how about doing it on the number of divisors, or on the number of prime factors?
 

Related Threads on Product of divisors number theory problem

Replies
8
Views
618
  • Last Post
Replies
2
Views
2K
Replies
6
Views
2K
Replies
3
Views
856
  • Last Post
Replies
19
Views
5K
  • Last Post
Replies
12
Views
3K
  • Last Post
Replies
4
Views
4K
Top