Let (a, b, c) denote a triplet of distinct integers in an ascending order.
If a²+ b²=c²+1
or if
a²+ b²=c²- 1
we will call such a triplet an ARAT (since it represents an almost-right-angle triangle) .
(4,8,9) is such a triplet.

How many ARATs are there, provided c<1,000,000?