Each of a, b, and c is a different base ten digit and n is a positive integer such that:

ab²+c²=ac²+cb²=n
For example:
27²+1²=21²+17²=730

Determine the total number of values of the positive integer constant n less than 2023, such that we will have valid values of a,b, and c satisfying the abovementioned condition.

***** No number can contain any leading zero.