I came across the Brahmagupta's identity mentioned here recently and thought it was pretty cool. https://en.wikipedia.org/wiki/Brahmagupta%27s_identity
It says - Numbers of the form a^2 + n*b^2 are closed under multiplication.
It says - Numbers of the form a^2 + n*b^2 are closed under multiplication.
In more advanced language: For R a commutative ring (like say, the integers) the following function f is a ring homomorphism
f:R[√(-n)] -> M_2(R),
f(a + b√(-n)) = [[a, (-n)b], [b, a]]