Question

What is the sum of all integer values of n such that 3n+15/(n−1)(n−5) is also an integer?
@hartnn
@him1618
@TuringTest

Answer 1

Anyone answer please...

Answer 2

As far as I've gotten (which is not much):
Find that:
\[
\frac{15}{n-5}-\frac{9}{n-1}
\]Is divisible by 2.

Answer 3

checking manually, o satisfies. wait for more and do reply...

Answer 4

n=2 also

Answer 5

It should be approachable by modular arithmetic, if you want to try that. Also, both fractions have to be of the same parity.

Answer 6

I have no idea of modulo arithmetic, i wud try gaining if u show ur approach..;.

Answer 7

n=3 , 4, -1,

Answer 8

-5 ,

Answer 9

7 as well.

Answer 10

n=10

Answer 11

-5
-1
0
2
3
4
7
10

Answer 12

That's all.

Answer 13

did u check by hand or some other method was followed by u??? please explain...

Answer 14

I checked it in C. There can't be any other solutions, anyways, but I am looking for a nice, mathematical solution.

Answer 15

O.k. thanx and one more ques... would u help???

Answer 16

Sure, go for it