Find N

Number Theory Level 2

Let $N$ be an integer between $200$ and $250$ such that

$N^3 - N^2 - N + 1$

is a perfect square. Find $N$ .

The answer is 224.

1 solution

Anand Babu Kotha
Jul 16, 2014

(N+1)(N-1)(N-1)=X^2

X = (N-1) √(N+1)

√(N+1) is also a perfect square

225 is a perfect square between 200-250

N=224