# Odd number of factors [Solved]Watch

#1
Hey,
I was wondering how I would describe a set of numbers where the number of factors is has is an odd number? Like how when the number of factors it has is 2, then its a prime number etc.
Here is the actual question:
The function d is defined as: d(n) = the number of factors of n, where n ∈ ℤ.
Describe the set of numbers for which d(n) is an odd number.

Rory

SOLVED: Square Numbers
Last edited by RoryDurrant; 3 months ago
1
3 months ago
#2
I think that I can see the answer.

Hint: In general, numbers have an even number of factors - can you see why? What would cause an odd number of them?
0
#3
Hey,
Not really sure, originally thought it was if they didnt contain 2, but then realised that prime numbers dont have the factor 2 and have an even number of factors?
Thanks
Last edited by RoryDurrant; 3 months ago
0
#4
Square numbers, got it
0
3 months ago
#5
(Original post by RoryDurrant)
Square numbers, got it
Note that the locker problem:

100 students are assigned lockers #1 through #100. The first student opens every locker. The second student closes every second locker (#2, #4, and on from there). The third student changes every third locker -- that is, the student will close every open locker he encounters and open every closed one. The fourth student changes every fourth locker, and so on, until all 100 students have taken their turn. How many lockers will be left open? Watch the video to figure out out to solve this puzzle, and to get the answer.

is essentially the same as the problem you've just solved.
0
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