Integer Integer!!

Number Theory Level 3

If $\frac{n+12}{n}$ is a integer

Find the summation for all possible number who satisfy $n$ as a integer.

\infty

1 56 30 28 0

1 solution

Md Mehedi Hasan
Oct 26, 2017

Here, $k=\frac{n+12}{n}=1+\frac{12}{n}$

so $k$ will be integer if $12$ is divisible by $n$

Now the product of $12$ is: $1,2,3,4,6,12$

so, $n=\pm1,\pm2,\pm3,\pm4,\pm6,\pm12$

Then the summation come $0$ ..

ohhh i forgot about the negatives

Aatmoshru Goswami - 10 months, 1 week ago