Square Pyramidal Number also Square

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Theorem

$4900$ is the only square pyramidal number which is also square:

$4900 = 70^2 = \ds \sum_{k \mathop = 1}^{24} k^2 = \dfrac {24 \paren {24 + 1} \paren {2 \times 24 + 1} } 6$


Proof




Sources