# 【星河（star）】题解([star] solution)-其他

## 【星河（star）】题解([star] solution)

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### Title:

A function \ (f (x) \) is defined as:

In particular, \ (f (0) = f (1) = 1 \). Small a gives a nonnegative integer \ (n \), please help him find the result of \ (f (n) \) modulo \ (998244353 \).

### Solution:

It can be found that except for \ (1,2,3 \), for \ (x \) is even, \ (f (x) = f (x + 1) \). Then \ (f (x + 2) \) is \ ((f (1) ++ F (X-2)) + F (x) = 2F (x) \), i.e. \ (f (x) = 2 ^ {\ frac {x} {2}-1} \). It can be solved by fast power. Proof can be regarded as mathematical induction.