Mathematics

Problem

Nicomachus was born in Roman Syria (now Jerash, Jordan) around 100 AD. He wrote in Greek and was a Pythagorean. He discovered an interesting number pattern involving cubes and the sums of odd numbers.

\begin{aligned} 1 &= 1^3 \\ 3 + 5 &= 8 = 2^3 \\ 7 + 9 + 11 &= 27 = 3^3 \\ &\vdots \end{aligned}

Find the series of odd numbers with sum equal to: a. a

5^3

b. b

7^3

c. c

12^3

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