Abstract
Polygonal numbers and sums of squares of primes are distinct fields of number theory. Here we consider sums of squares of consecutive (of order and rank) polygonal numbers. We try to express sums of squares of polygonal numbers of consecutive orders in matrix form. We also try to find the solution of a Diophantine equation in terms of polygonal numbers.
Highlights
Polygonal numbers and sums of squares of primes are distinct fields of number theory
The right triangles immediately remind us of Pythagorean property. This leads to the idea of finding sums of squares of consecutive polygonal numbers
We calculate the sums of squares of m-gonal numbers of consecutive ranks
Summary
Polygonal numbers and sums of squares of primes are distinct fields of number theory. Polygonal Numbers, Sums of Squares, Triangular Numbers The concept of polygonal numbers was first defined by the Greek Mathematical hypsicles in the year 170 BC. This leads to the idea of finding sums of squares of consecutive polygonal numbers.
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