Discrete Math Help

**Hornedog20** · November 2nd 2008, 10:50 AM

I am new to Discrete Math. I am able to figure out how to do 1, 2, and 4 of the attachment, but do not have a clue where to start on the rest of the problems. Any help at all would be great. Thanks in advance.

**Soroban** · November 2nd 2008, 12:06 PM

Hello, Hornedog20!

3. What is the largest divisor of $n^7 - n^3$ for all $n \in N$ ?
Are you sure of the wording?
The largest divisor of ${\color{blue}n^7-n^3}$ is, of course: . ${\color{blue}n^7-n^3}$

Factor: . $n^7-n^3 \;=\;n^3(n^4-1) \;=\;n^3(n^2-1)(n^2+1) \;=\;n^3(n-1)(n+1)(n^2+1)$

Then $n^2+1$ is the largest prime factor.

**Hornedog20** · November 2nd 2008, 05:22 PM

Thanks for the reply. That is what I was thinking for #3 as well. I believe I have figured out 5, 6, and 7 now as well. I still am having problems with 8 and 9 though.

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