Recently, I had problem: counting ways in which X could be represented as summing Fibonacci numbers without repeating them. With X <= 1e9;and the input has N text with N <= 1e5. Can you give me an idea to solve this problem? thanks for help.

The other day I met a problem that needed to count the number of primes less than n with n <= 1e10. But I only know how to use sieve to solve but it can only run with n <= 1e6. Can you help me find a better solution? thanks for help!