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 when the base is odd... by pcbouhid)

When the base b is even, b=2k, say, then 2005=16kł+5 and is congruent to 5 mod 8 and therefore cannot be a square as it is well known that the square of an odd number is congruent to 1 mod 8.

Posted by Richard on 2005-05-30 22:05:55