Assume toward a contradiction that
x
is an integer satisfying
2
x
+ 1 = 5
x
– 4.
Reducing the equation modulo 3 gives
2
x
+ 1 ≡ 2
x
+ 2 mod 3.
Subtracting 2
x
from both sides leaves 1 ≡ 2 mod 3, which is a contradiction.
