# help would be appreciated, thanks!

• Sep 14th 2007, 06:27 AM
mich13
help would be appreciated, thanks!
as n takes each positive integer value in turn (that is n=1, n=2, n=4 and so on) how many different values are obtained for the remainder when n(squared) is divede by n+4?

a)1 b)8 c)9 d)16 e) infinitely many

:confused::confused::confused:
help would be appreciated, thanks!

xxx
• Sep 14th 2007, 09:06 AM
topsquark
Quote:

Originally Posted by mich13
as n takes each positive integer value in turn (that is n=1, n=2, n=4 and so on) how many different values are obtained for the remainder when n(squared) is divede by n+4?

a)1 b)8 c)9 d)16 e) infinitely many

:confused::confused::confused:
help would be appreciated, thanks!

xxx

So for n being an integer what are the possible remainders for:
$\displaystyle \frac{n^2}{n + 4}$

Start by looking at n = 1:
$\displaystyle \frac{1^2}{1 + 4} = \frac{1}{5}$
so the remainder is 1.

n= 2: $\displaystyle \frac{2^2}{2 + 4} = \frac{4}{6}$ so the remainder is 4. (No simplifying the fraction!)

n= 3: $\displaystyle \frac{3^2}{3 + 4} = \frac{9}{7}$ so the remainder is 2.

n= 4: $\displaystyle \frac{4^2}{4 + 4} = \frac{16}{8}$ so the remainder is 0.

n= 5: $\displaystyle \frac{5^2}{5 + 4} = \frac{25}{9}$ so the remainder is 7.

Continue by doing the long division:
$\displaystyle \frac{n^2}{n + 4} = n - 4 + \frac{16}{n + 4}$

Does this help?

-Dan
• Sep 15th 2007, 12:01 PM
mich13
?
noo it ddnt help :(
im 13 i dnt get a WORD of that lol
but thanks anywways.. i appreciate your time xxx
• Sep 15th 2007, 12:25 PM
Krizalid
Quote:

Originally Posted by topsquark
Continue by doing the long division:
$\displaystyle \frac{n^2}{n + 4} = n - 4 + \frac{16}{n + 4}$

Well, you can also do this without long division :D

$\displaystyle \frac{{n^2 }} {{n + 4}} = \frac{{(n + 4)(n - 4) + 16}} {{n + 4}} = n - 4 + \frac{{16}} {{n + 4}}$

Though I don't think you used long division for this :)

--

mich13, I suggest you appreciate the help, read carefully. Our help it depends of the time.
• Sep 15th 2007, 12:54 PM
topsquark
Quote:

Originally Posted by mich13
noo it ddnt help :(
im 13 i dnt get a WORD of that lol
but thanks anywways.. i appreciate your time xxx

I simply considered the cases for n = 1 to n = 5. This is just division. My point is, what is the remainder when n is larger than 12? Try a few of these.

-Dan