Question 7
A perfect square $N$ is called a “BIMC number” if there exist three positive integers $a$, $b$ and $c$, where $a\lt b\lt c$, such that
$$N=(b-a)(c-a)(c-b)=ab+ac+bc.$$
For example, $230400$ is a BIMC number since $230400=480\times480$ and
$$230400=(288-224)(324-224)(324-288)$$
$$=224\times288+224\times324+288\times324.$$
What is the smallest BIMC number?
$$N=(b-a)(c-a)(c-b)=ab+ac+bc.$$
For example, $230400$ is a BIMC number since $230400=480\times480$ and
$$230400=(288-224)(324-224)(324-288)$$
$$=224\times288+224\times324+288\times324.$$
What is the smallest BIMC number?