A.J. Meyl proved in 1878 that only three tetrahedral numbers are also perfect squares, namely:

T1 = 1^2 = 1

T2 = 2^2 = 4

T48 = 140^2 = 19600.

The only tetrahedral number that is also a square pyramidal number is 1 (Beukers, 1988), and the only tetrahedral number that is also a perfect cube is 1.

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