{"problem":{"name":"Polynomial Divisors","description":{"content":"You are given a polynomial of degree $N$ with integer coefficients: $f(x)=a_Nx^N+a_{N-1}x^{N-1}+...+a_0$. Find all prime numbers $p$ that divide $f(x)$ for every integer $x$.","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"tenka1_2019_e"},"statements":[{"statement_type":"Markdown","content":"You are given a polynomial of degree $N$ with integer coefficients: $f(x)=a_Nx^N+a_{N-1}x^{N-1}+...+a_0$. Find all prime numbers $p$ that divide $f(x)$ for every integer $x$.\n\n## Constraints\n\n*   $0 \\leq N \\leq 10^4$\n*   $|a_i| \\leq 10^9(0\\leq i\\leq N)$\n*   $a_N \\neq 0$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$a_N$\n$:$\n$a_0$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"tenka1_2019_e","tags":[],"sample_group":[["2\n7\n-7\n14","2\n7\n\n$2$ and $7$ divide, for example, $f(1)=14$ and $f(2)=28$."],["3\n1\n4\n1\n5","There may be no integers that satisfy the condition."],["0\n998244353","998244353"]],"created_at":"2026-03-03 11:01:14"}}