1982 AHSME Problems/Problem 26
Problem 26
If the base representation of a perfect square is
, where
, then
equals
Partial and Wrong Solution
From the definition of bases we have , and
If , then
, which makes
If , then
, which clearly can only have the solution
, for
. This makes
, which doesn't have 4 digits in base 8
If , then
, which clearly can only have the solution
, for
.
is greater than
, and thus, this solution is invalid.
If , then
, which clearly has no solutions for
.
Similarly, yields no solutions
If , then
, which clearly can only have the solution
, for
. This makes
, which doesn't have 4 digits in base 8.
If , then
, which clearly can only have the solution
, for
. This makes
, which doesn't have 4 digits in base 8