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
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Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $4900$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $4900$