f(n+1)=nf(n)

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

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

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

Multiply fn * n
1f + fn = fn2

Solving
1f + fn = fn2

Solving for variable 'f'.

Move all terms containing f to the left, all other terms to the right.

Add '-1fn2' to each side of the equation.
1f + fn + -1fn2 = fn2 + -1fn2

Combine like terms: fn2 + -1fn2 = 0
1f + fn + -1fn2 = 0

Factor out the Greatest Common Factor (GCF), 'f'.
f(1 + n + -1n2) = 0

Subproblem 1
Set the factor 'f' equal to zero and attempt to solve:

Simplifying
f = 0

Solving
f = 0

Move all terms containing f to the left, all other terms to the right.

Simplifying
f = 0
Subproblem 2
Set the factor '(1 + n + -1n2)' equal to zero and attempt to solve:

Simplifying
1 + n + -1n2 = 0

Solving
1 + n + -1n2 = 0

Move all terms containing f to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + n + -1 + -1n2 = 0 + -1

Reorder the terms:
1 + -1 + n + -1n2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + n + -1n2 = 0 + -1
n + -1n2 = 0 + -1

Combine like terms: 0 + -1 = -1
n + -1n2 = -1

Add '-1n' to each side of the equation.
n + -1n + -1n2 = -1 + -1n

Combine like terms: n + -1n = 0
0 + -1n2 = -1 + -1n
-1n2 = -1 + -1n

Add 'n2' to each side of the equation.
-1n2 + n2 = -1 + -1n + n2

Combine like terms: -1n2 + n2 = 0
0 = -1 + -1n + n2

Simplifying
0 = -1 + -1n + n2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
f = {0}