Abstract
In this paper, special 2-tuples with elements stand well-known polynomials and polygonal numbers with different sides that exclusively meet the property that the summation or difference of two elements provides a square can be stretched to 3-tuples but not 4-tuples with the same characteristics are displayed. Also, the similar characteristics of all such 3-tuples are checked with numerical values by Python programs. KEYWORDS: Diophantine m-tuples, Congruence relations, polygonal numbers, polynomials
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