Consider a base-N nonzero perfect square of the form X₁X₁X₂X₂, where X₁ and X₂ are base-N digits whether same or different.

Derive a general formula that expresses X₁X₁X₂X₂ in terms of N, where N is an integer > 3.

*** X₁X₁X₂X₂ is a concatenation of the digits and not the product.