# High school math questions, algebra.

the difference between a positive integer, n, and its cube is 4896. Compute n. Please give solution and detailed explanation! Thank you ver much! I tried and got 17, but what i did is to try numbers one by one, so i would really appreciate if anyone can tell me the right and systematic way to tackle this question??

• What if someone asks "Product of three successive integers is $4896$. What is the middle number?"? Hint: Prime factorization of $4896$. – Alistair Nov 4 '14 at 2:15
• You can factor 4896 but since (n-1)n(n+1) is close to the cube root of 4896 and started from that. Rounded 16.5+ to 17 and showed that 16*17*18 equals 4896. Although I guessed n = 17 it was an easy and fast guess to fit the three successive factors formula. – K7PEH Nov 4 '14 at 2:18

$\textbf{HINT-}$ you have to solve $n^3-n-4896=0$. $n=17$ is the only real solution to this cubic. So there are none other.