find-all-f-N-N-such-that-f-n-f-n-2f-n-

Question Number 680 by 123456 last updated on 23/Feb/15

f i n d a l l f : N \to N s u c h t h a t

f [n + f (n)] = 2 f (n)

Answered by prakash jain last updated on 23/Feb/15

f (n) = k n + k_{1}

f (n + k n + k_{1}) = k (k + 1) n + {k k}_{1} = 2 k n + 2 k_{1}

k = 1, k_{1} = 0

k = 0, k_{1} = 0

f (n) = n

or f (n) = 0