A morphic number is a real number 
for which there exist positive
integers 
and 
such that
 |  |  |
(1)
|
 |  |  |
(2)
|
Thus both 
and 
are integer powers of 
(Aarts et al. 2001, p. 57).
The only morphic numbers are the golden ratio 
and the plastic
constant 
(Aarts et al. 2001, p. 58). The golden ratio
satisfies 
and 
,
so has 
.
The plastic constant satisfies 
and 
, so has 
.
