f(f(f(n)))=f(n+1)+1

Solution for f(f(f(n)))=f(n+1)+1 equation:

Simplifying
f(f(f(n))) = f(n + 1) + 1

Multiply f * n
f(f(fn)) = f(n + 1) + 1

Multiply f * fn
f(f2n) = f(n + 1) + 1

Multiply f * f2n
f3n = f(n + 1) + 1

Reorder the terms:
f3n = f(1 + n) + 1
f3n = (1 * f + n * f) + 1
f3n = (1f + fn) + 1

Reorder the terms:
f3n = 1 + 1f + fn

Solving
f3n = 1 + 1f + fn

Solving for variable 'f'.

Reorder the terms:
-1 + -1f + -1fn + f3n = 1 + 1f + fn + -1 + -1f + -1fn

Reorder the terms:
-1 + -1f + -1fn + f3n = 1 + -1 + 1f + -1f + fn + -1fn

Combine like terms: 1 + -1 = 0
-1 + -1f + -1fn + f3n = 0 + 1f + -1f + fn + -1fn
-1 + -1f + -1fn + f3n = 1f + -1f + fn + -1fn

Combine like terms: 1f + -1f = 0
-1 + -1f + -1fn + f3n = 0 + fn + -1fn
-1 + -1f + -1fn + f3n = fn + -1fn

Combine like terms: fn + -1fn = 0
-1 + -1f + -1fn + f3n = 0

The solution to this equation could not be determined.