Language: C++

#include <bits/stdc++.h>

using namespace std;
using Int = long long;

// Modulo.h start----------------------------------------

#pragma once

#include <vector>

unsigned int mod;
struct Modint;
std::vector<Modint> fact_mod;
std::vector<Modint> rev_fact_mod;

using namespace std;

template<typename Tint>
Tint gcd(Tint a, Tint b) {
	// O(log max(a,b))
	return b != 0 ? gcd(b, a % b) : a;
}

template<typename Tint>
Tint lcm(Tint a, Tint b) {
	return a / gcd(a, b) * b;
}

// a x + b y = gcd(a, b)
int extgcd(const unsigned int a, const unsigned int b, int &x, int &y) {
	// O(log max(a,b))
	int g = a; x = 1; y = 0;
	if (b != 0) g = extgcd(b, a % b, y, x), y -= (a / b) * x;
	return g;
}

void set_mod(const unsigned int m) {
	mod = m;
}
void set_mod(const int m) {
	if (m > 0)
		set_mod((unsigned int)m);
	else
		cout << "Error in set_mod" << endl;
}

unsigned int inv_mod(const unsigned int a) {
	int x, y;
	if (extgcd(a, mod, x, y) == 1)
		return (unsigned int)(((long long)x + mod) % mod);
	else // unsolvable
		return 0;
}

struct Modint {
	unsigned int value;
	Modint() { }
	Modint(unsigned int value) : value(value%mod) {	}
	Modint(int value) : Modint((unsigned int)(value % mod + mod)) {	}
	Modint(const Modint& rhs) : Modint(rhs.value) { }
	bool operator==(const Modint& rhs) const;
	inline bool operator!=(const Modint& rhs) const
	{
		return !(*this == rhs);
	}
	Modint& operator+=(const Modint& rhs);
	Modint& operator+=(const unsigned int rhs);
	Modint& operator+=(const int rhs);
	Modint& operator-=(const Modint& rhs);
	Modint& operator-=(const unsigned int rhs);
	Modint& operator-=(const int rhs);
	Modint& operator*=(const Modint& rhs);
	Modint& operator*=(const unsigned int rhs);
	Modint& operator*=(const int rhs);
	Modint& operator/=(const Modint& rhs);
	Modint& operator/=(const unsigned int rhs);
	Modint& operator/=(const int rhs);
};
bool Modint::operator==(const Modint& rhs) const
{
	return value == rhs.value;
}
Modint& Modint::operator+=(const Modint& rhs)
{
	(*this) += rhs.value;
	return *this;
}
Modint& Modint::operator+=(const unsigned int rhs)
{
	unsigned long long tmp = this->value;
	tmp += rhs;
	tmp %= mod;
	this->value = (unsigned int)tmp;
	return *this;
}
Modint& Modint::operator+=(const int rhs)
{
	(*this) += (unsigned int)(rhs % mod + mod);
	return *this;
}
Modint& Modint::operator-=(const Modint& rhs)
{
	(*this) -= rhs.value;
	return *this;
}
Modint& Modint::operator-=(const unsigned int rhs)
{
	*this += mod - rhs % mod;
	return *this;
}
Modint& Modint::operator-=(const int rhs)
{
	*this -= (unsigned int)(rhs % mod + mod);
	return *this;
}
Modint& Modint::operator*=(const Modint& rhs)
{
	(*this) *= rhs.value;
	return *this;
}
Modint& Modint::operator*=(const unsigned int rhs)
{
	unsigned long long tmp = this->value;
	tmp *= rhs;
	tmp %= mod;
	this->value = (unsigned int)tmp;
	return *this;
}
Modint& Modint::operator*=(const int rhs)
{
	(*this) *= (unsigned int)(rhs % mod + mod);
	return *this;
}
Modint& Modint::operator/=(const Modint& rhs)
{
	(*this) /= rhs.value;
	return *this;
}
Modint& Modint::operator/=(const unsigned int rhs)
{
	*this *= inv_mod(rhs);
	return *this;
}
Modint& Modint::operator/=(const int rhs)
{
	*this /= (unsigned int)(rhs % mod + mod);
	return *this;
}
const Modint operator + (const Modint& lhs, const Modint& rhs) {
	return Modint(lhs) += rhs;
}
const Modint operator + (const Modint& lhs, unsigned int rhs) {
	return Modint(lhs) += rhs;
}
const Modint operator + (unsigned int lhs, const Modint& rhs) {
	return Modint(lhs) += rhs;
}
const Modint operator - (const Modint& lhs, const Modint& rhs) {
	return Modint(lhs) -= rhs;
}
const Modint operator - (const Modint& lhs, unsigned int rhs) {
	return Modint(lhs) -= rhs;
}
const Modint operator - (unsigned int lhs, const Modint& rhs) {
	return Modint(lhs) -= rhs;
}
const Modint operator * (const Modint& lhs, const Modint& rhs) {
	return Modint(lhs) *= rhs;
}
const Modint operator * (const Modint& lhs, unsigned int rhs) {
	return Modint(lhs) *= rhs;
}
const Modint operator * (unsigned int lhs, const Modint& rhs) {
	return Modint(lhs) *= rhs;
}
const Modint operator / (const Modint& lhs, const Modint& rhs) {
	return Modint(lhs) /= rhs;
}
const Modint operator / (const Modint& lhs, unsigned int rhs) {
	return Modint(lhs) /= rhs;
}
const Modint operator / (unsigned int lhs, const Modint& rhs) {
	return Modint(lhs) /= rhs;
}
ostream& operator<<(std::ostream& lhs, const Modint& rhs)
{
	lhs << rhs.value;
	return lhs;
}

Modint pow_mod(const Modint& x, const unsigned int k) { //x^k (mod)
	if (k == 0)     return Modint(1);
	if (k % 2 == 0) return pow_mod(x*x, k / 2);
	else            return x * pow_mod(x, k - 1);
}
Modint pow_mod(const unsigned int x, const unsigned int k) {
	return pow_mod(Modint(x), k);
}

std::vector<Modint> set_fact_mod(unsigned int n) {
	fact_mod = vector<Modint>(n + 1);
	fact_mod[0] = 1;
	for (unsigned int i = 1; i <= n; i++)
	{
		fact_mod[i] = fact_mod[i - 1] * i;
	}
	return fact_mod;
}

std::vector<Modint> set_rev_fact_mod(unsigned int n) {
	rev_fact_mod = vector<Modint>(n + 1);
	rev_fact_mod[n] = 1 / fact_mod[n];
	for (int i = n - 1; i >= 0; i--)
	{
		rev_fact_mod[i] = rev_fact_mod[i + 1] * (unsigned int)(i + 1);
	}
	return rev_fact_mod;
}

Modint combination_mod_precalculation(unsigned int n, unsigned int r) {
	//set mod, fact_mod, rev_fact_mod
	return fact_mod[n] * rev_fact_mod[r] * rev_fact_mod[n - r];
}

Modint combination_mod_straightforward(unsigned int n, unsigned int r) { //mod is prime
	if (r * 2 > n) r = n - r;
	Modint numerator = 1;
	Modint denominator = 1;
	for (unsigned int i = 1; i <= r; ++i) {
		numerator *= n - i + 1;
		denominator *= i;
	}
	return numerator / denominator;
}

// Modulo.h end----------------------------------------------

vector<bool> is_primes;

void set_is_primes(unsigned int n) {
	is_primes.assign(n + 1, true);
	for (unsigned int i = 0; i <= min((unsigned int)1, n); ++i)
		is_primes[i] = false;
	for (unsigned int i = 2; i*i <= n; ++i)
		if (is_primes[i])
			for (unsigned int j = i * i; j <= n; j += i)
				is_primes[j] = false;
}

unordered_map<unsigned int, unsigned int> make_prime_factors(unsigned int n, const bool is_using_primes) {
	//O(sqrt(n))
	unordered_map<unsigned int, unsigned int> prime_factors;
	for (unsigned int i = 2; i*i <= n; i++) {
		if (is_using_primes && !is_primes[i])
			continue;
		while (n % i == 0) {
			++prime_factors[i];
			n /= i;
		}
	}
	if (n != 1)
		++prime_factors[n];
	return prime_factors;
}

int main() {
	unsigned int N;
	cin >> N;
	vector<int> a(N + 1, 0);
	for (int i = N; i >= 0; i--)
	{
		cin >> a[i];
	}

	vector<int> ans;
	set_is_primes(N);
	for (unsigned int p = 2; p <= N; p++)
	{
		if (!is_primes[p])
			continue;

		set_mod(p);
		vector<Modint> ma;
		for (unsigned int i = 0; i <= N; i++)
		{
			ma.push_back(a[i]);
		}
		for (int n = N - p; n >= 0; n--)
		{
			ma[n + 1] += ma[n + p];
		}

		bool is_divided = true;
		for (int i = p - 1; i >= 0; i--)
		{
			if (ma[i] != 0) {
				is_divided = false;
				break;
			}
		}
		if (is_divided)
			ans.push_back(p);
	}

	int g = a[0];
	for (unsigned int i = 1; i < N; i++)
	{
		g = gcd(g, abs(a[i]));
	}
	unordered_map<unsigned int, unsigned int> prime_factors = make_prime_factors(g, false);
	for (const auto& d : prime_factors)
	{
		if (d.first <= N)
			continue;
		ans.push_back(d.first);
	}
	sort(ans.begin(), ans.end())

	for (const int p : ans)
	{
		cout << p << endl;
	}

	return 0;
}



Compiler output:
a.cc:8:9: warning: #pragma once in main file
    8 | #pragma once
      |         ^~~~
a.cc: In function 'int main()':
a.cc:318:37: error: expected ';' before 'for'
  318 |         sort(ans.begin(), ans.end())
      |                                     ^
      |                                     ;
  319 | 
  320 |         for (const int p : ans)
      |         ~~~