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Find the number of functions that map non-negative integers to non-negative integers such that
Notes:
By map non-negative integers to non-negative integers , we mean that the domain and range of are both the set of non-negative integers.
The answer is 0.
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1 solution
f ( f ( x ) ) = x + 2 0 1 5
Substitute x = 2 0 1 5 , f ( f ( f ( x ) ) ) = f ( x ) + 2 0 1 5 f ( x + 2 0 1 5 ) = f ( x ) + 2 0 1 5
Now it is clear that no function is possible such that it satisfies this equation and map non-negative integers to non-negative integers.