Find all integers \(n\) such that the arithmetic mean of all its factors is an integer.


Thanks so much!

 Mar 13, 2022

Every odd prime number has two factors and only two factors, 1 and the prime number.

The result of adding 1 to the odd prime number is an even number; dividing this 

answer by 2 results in an integer.

Now, you have an infinite number of answers.

And yet, there are more; some even numbers also fulfill the requirement ...

 Mar 14, 2022

Oh! That's really cool! I haven't thought of the odd primes.


I also assume that some non-odd primes work and as you say, some even numbers work too. Is there a specific way of describing them or is it just at random?


Thank you so much,geno3141!

ibhar  Mar 14, 2022

Thanks Geno,

I think your answer is cool too :)


Attn:  ibhar,

Thank you for responsing to Gino's answer so nicely.   laugh


You need to think.

Your statement:   "I also assume that some non-odd primes work"

1) Firstly, tell me some non-odd primes.

2) second show me with one of them what the average of its factors is. 

3) discuss your answers.


YES  you are expected to answer me :)

Melody  Mar 14, 2022
edited by Melody  Mar 14, 2022

1 Online Users