Palindromic Cube with Non-Palindromic Root
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Theorem
The only known palindromic cube with a root that is not itself palindromic is $10 \, 662 \, 526 \, 601$.
Proof
We have that:
- $10 \, 662 \, 526 \, 601 = 2201^3$
There are no others whose cube root is below $10^{15}$.
Sources
- 1970: G.J. Simmons: Palindromic powers (J. Recr. Math. Vol. 3, no. 2: pp. 93 – 98)
- 1972: G.J. Simmons: On palindromic squares of non-palindromic numbers (J. Recr. Math. Vol. 5, no. 1: pp. 11 – 19)
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $10,662,526,601$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $10,662,526,601$