$\textbf{Problem 16:}$Find all functions $f : Z \to Z$ with the property that for any surjective function
$g : Z \to Z$, the function $f + g$ is also surjective.
Search found 2 matches
- Mon Jun 21, 2021 1:06 pm
- Forum: National Math Camp
- Topic: Special Problem Marathon
- Replies: 38
- Views: 34070
- Sat Jun 19, 2021 11:25 pm
- Forum: National Math Camp
- Topic: Special Problem Marathon
- Replies: 38
- Views: 34070
Re: Special Problem Marathon
$\textbf{Problem 15 :}$ Let $c, d \geqslant 2$ be positive integers.Let $\{a_n\}$ be the sequence which satisfies $a_1=c$, $a_{n+1}=a_n^{d}+c$ for every $n \geqslant 1$. Prove that for any $n \geqslant 2$, there exists a prime number $p$ such that $p \mid a_n$ and $p \nmid a_i$ for $i=1,2,\dots,n-1...