Question 75
Prove that for every positive integer $n$ the number
$$
N = \underbrace{44\dots4}_{n} \underbrace{88\dots8}_{n} - 1 \underbrace{33\dots3}_{n-1} 2,
$$
is a perfect square.
$$
N = \underbrace{44\dots4}_{n} \underbrace{88\dots8}_{n} - 1 \underbrace{33\dots3}_{n-1} 2,
$$
is a perfect square.