Abstract: This study identifies the rectangles with dimensions and such that the expression , is represented by digit Spy number and Automorphic number. A and S denotes the area and semi-perimeter of the rectangle. Total number of rectangles satisfying the above relations are obtained.
Furthermore, both primitive and non-primitive rectangles are accounted for in the total tally of solutions derived from the proposed relationship.

Keywords: Automorphic number, primitive, non-primitive and Spy number.

Downloads: | DOI: 10.17148/IARJSET.2026.13326