2005 base 10 is not a square. Neither is 2005 base 7 a square (equal 2*7^3+5=691). Is there any base b such that 2005 base b is a square?

(In reply to Possibly? by Michael S. McCracken)

Ha, ha!  Nice try!  "Just Math" morphed into "Riddles"!  The language of mathematics uses "base" with more than one meaning depending on the context.  You invoked the logarithim "base" instead of the number representation "base".  Can you find another solution "based" on yet another mathematical definition of "base"?  Well, I'll be darned!  I just thought of one!

Posted by McWorter on 2005-05-31 17:32:27