Find the number of ordered triples $(a,b,c)$ of integers satisfying $0\le a,b,c\le 1000$ and \$$(a+b+c-1)(a^2+b^2+c^2+3(ab+bc+ca)) \equiv 3(a+b+c)(ab+bc+ca) \pmod{1001}$$
I am totally clueless how to solve this, as I am new to number theory.
So, any hint will be appreciated.