If n is a positive integer such as(adsbygoogle = window.adsbygoogle || []).push({});

[tex]2{\leq}n{\leq}80[/tex]

For how many values the expression [tex]\frac{(n+1)n(n-1)}{8}[/tex] takes positive and integer values?

I solved it that way...

[tex]\frac{(n+1)n(n-1)}{8}=\frac{(n^{2}-1)n}{8}[/tex]

(n^2 - 1)n must have 8 as one of its factor.

Either n is a multiple of 8, or n^2 - 1 is. Also the case were n^2 - 1 has 4 as one of its factors, n having 2, and vice-versa, is impossible - if n^2 - 1 is even, n is odd, and vice-versa.

So every mutliple of 8 up to 80 is a possible value. So there is 10 values.

Let's list those numbers

8, 16 , 24 , 32 , 40 , 48 , 56 , 64 , 72, 80

Add one to each one of these values

9, 17, 25, 33, 41, 49, 65 , 73, 81

There is 4 perfect square in this list. So if n^2 - 1 is a multiple of 8, then there is 4 possible values for n.

10 + 4 = 14

So 14 possibilities in total. But the true awnser is not what I found. What is wrong in my reasoning?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Complex integer expression problem

**Physics Forums | Science Articles, Homework Help, Discussion**