1972 AHSME Problems/Problem 11
Problem
The value(s) of for which the following pair of equations
may have a real common solution, are
Solution
We can rewrite the equation as
, or
Then
. Testing all the residues modulo 11, we find that the only solution to
is
, so
.
Now, since 7 is a digit in base and base
, we must have
. We must also have
, so
. We can have equality with
, so the least possible value of
is
.