Number theory!

Number Theory Level 4

$\large t=\frac{n^3}{n-a}, \quad a\leq 5$

The above equation holds true for some positive integers $t$ , $n$ , and $a$ . Let $S$ be the sum of all distinct values of $n$ . Find $(S-1)$ .

1 solution

Kushal Bose
Jul 22, 2016

$t=\dfrac{n^3}{n-a}$

$t=\dfrac{n^3-a^3+a^3}{n-a}$

$t=n^2+an+a^2$ + $\dfrac{a^3}{n-a}$

Now putting a=1,2,3,4,5 one can find the distinct values of n for which second part will be an integer

Values of n are 2,3,4,5,6,8,10,12,20,30,36,68,130

how did u plugged values of a

Adi Garg - 4 years, 10 months ago

Your second step is very nice.

Priyanshu Mishra - 4 years, 10 months ago

Did the same

Sayantan Saha - 4 years, 10 months ago

Why can't we substitute the values directly?

Racchit Jain - 4 years, 10 months ago