Number Theory

    

The Power Theorem: Sum of Consecutive Powers as Perfect Squares

Authors: Manikandan Karunanidhi

This work introduces a new family of natural numbers for which the sum of two successive powers, beginning with an even exponent, results in a perfect square. The identity is derived from the condition where the base plus one equals a perfect square. A formal proof is presented, along with a recurrence relation and supporting computational evidence in tabular form. This study contributes to the field of number theory by highlighting an unexpected relationship between exponential expressions and perfect squares.

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[v1] 2025-11-11 21:17:49

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