Nicomachus was born in Roman Syria (now Jerash, Jordan) around 100 AD

MATHEMATICS · Multi-part · CBSE · Mathematics · Number Play · Number Play

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. 1=133+5=8=237+9+11=27=33⋮\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: (1) a 535^3 (2) b 737^3 (3) c 12312^3

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