Posted by **rohit** on Wednesday, April 10, 2013 at 6:35am.

What is the sum of all integer values of n such that 3n+15/(n−1)(n−5) is also an integer

- maths -
**Steve**, Wednesday, April 10, 2013 at 11:10am
since (n-1)(n-5) <= 3n+15 for -1 <= n <= 10, that limits our choices

listing the values of n, (3n+15) and (n-1)(n-5), we have

-1 12 14 no

0 15 5 YES

1 18 0 no

2 21 -3 YES

3 24 -4 YES

4 27 -3 YES

5 30 0 no

6 33 5 no

7 36 12 YES

8 39 21 no

9 42 32 no

10 45 45 YES

0+2+3+4+7+10 = 26

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