Nicomachus's theorem is the identity stating that the sum of the first n cubes equals the square of the nth triangular number, so that 1 cubed plus 2 cubed plus 3 cubed and so on up to n cubed equals the square of the sum 1 plus 2 plus 3 up to n. The identity is attributed to Nicomachus of Gerasa, who lived from around 60 to 120 CE and observed that summing consecutive blocks of odd numbers produces successive cubes, without giving a formal proof of the pattern himself.
Facts
Classification
Statement Form Proof Method Connections
Has Statement Form
In Branch
Source Squared triangular number (Wikipedia)
Sources
1. Squared triangular number (Wikipedia)
In Group: Binomial and Summation Identities, Lead
This identity is sometimes called Nicomachus's theorem, after Nicomachus of Gerasa
In Branch: Number Theory, Lead sentence
In number theory, the sum of the first n cubes is the square of the nth triangular number.
View the Source2. ProofWiki: Nicomachus's Theorem - ProofWiki
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