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?

It was stated only "a square" !!!! It was not tacitily stated "a square of an integer, or a square of a rational number, etc..."

So :

Since the left side of 2*b^3 + 5 = a^2 is odd, if a = n*i, the right side could be odd too, = - n^2.

There are infinite bases, and the first integer base, making n = 7 is b = -3.

Posted by pcbouhid on 2005-06-04 23:16:40