Strictly non-palindromic number: Difference between revisions

Revision as of 12:09, 16 July 2005

Revision as of 19:55, 8 January 2006

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==Properties==

All strictly non-palindromic numbers beyond 6 are [[prime number|prime]]. To see why composite ''n'' > 6 cannot be strictly non-palindromic, for each such ''n'' a base ''b'' must be shown to exist where ''n'' is palindromic.

* If ''n'' is [[even]], then ''n'' is written 22 (a palindrome) in base ''b'' = ''n''/2 − 1.

Otherwise ''n'' is [[odd]]. Write ''n'' = ''p'' · ''m'', where ''p'' is the smallest odd prime factor of ''n''. Then clearly ''p'' ≤ ''m''.