Palindromic Cube with Non-Palindromic Root

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): $10,662,526,601$
This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.