A unified approach is presented for determining all the constants
γ
m
,
n
(
m
≥
0
,
n
≥
0
)
{\gamma _{m,n}}\;(m \geq 0,n \geq 0)
which occur in the study of real vs. complex rational Chebyshev approximation on an interval. In particular, it is shown that
γ
m
,
m
+
2
=
1
/
3
(
m
≥
0
)
{\gamma _{m,m + 2}} = 1/3\;(m \geq 0)
, a problem which had remained open.