Problem p03065 (python)

Fixed submission:
import sys
from fractions import gcd
n = int(input())
a = [int(input()) for _ in range(n+1)]
x = 0
while True:
	m = abs(sum([a[i]*pow(x, n-i) for i in range(n+1)]))
	if m != 0:
		break
	x += 1
ps = []

i = 2
while i**2 <= m and i <= n+1:
#for i in range(2, int(sqrt(m))+1):
	if m%i == 0:
		ps.append(i)
		while m%i == 0:
			m //= i
	i += 1
if m != 1 and n != 0:
	ps.append(m)
#print(ps)
g = a[0]
for i in range(1, n+1):
	g = gcd(g, abs(a[i]))

#print(g)
ans = []

i = 2
while i**2 <= g:
#for i in range(2, int(sqrt(m))+1):
	if g%i == 0:
		if i >= n+1:
			ans.append(i)
		while g%i == 0:
			g //= i
	i += 1
if g != 1 and g >= n+1:
	ans.append(g)

a = a[::-1]
for p in ps:
	if p-1 > n:
		ng = False
		for i in range(1, n+1):
			if a[i]%p != 0:
				ng = True
				break
		if not ng:
			ans.append(p)
	else:
		mods = [0 for _ in range(p-1)]
		for i in range(1, n+1):
			mods[i%(p-1)] += a[i]
			mods[i%(p-1)] %= p
		if mods[0] == 0:
			ng = False
			for i in range(1, p-1):
				if mods[i] != 0:
					ng = True
					break
			if not ng:
				ans.append(p)
ans = sorted(list(set(ans)))
if ans:
	print(*ans, sep="\n")

Buggy submission (verdict: Runtime Error):
import sys
from math import sqrt
from fractions import gcd
n = int(input())
a = [int(input()) for _ in range(n+1)]
m = a[0]
for i in range(1, n+1):
	m = gcd(m, abs(a[i]))
ps = []

i = 2
while i**2 <= m:
#for i in range(2, int(sqrt(m))+1):
	if m%i == 0:
		ps.append(i)
		while m%i == 0:
			m //= i
	i += 1
if m != 1:
	ps.append(m)

prime = []
for i in range(2, n+1):
	for p in prime:
		if i%p == 0:
			break
	else:
		prime.append(i)

ps = sorted(list(set(ps + prime)))
if n == 0:
	if ps:
		print(*ps, sep="\n")
	sys.exit()
a = a[::-1]
for p in ps:
	if p-1 > n:
		ng = False
		for i in range(1, n+1):
			if a[i]%p != 0:
				ng = True
				break
		if not ng:
			print(p)
	else:
		mods = [0 for _ in range(p-1)]
		for i in range(1, n+1):
			mods[i%(p-1)] += a[i]
			mods[i%(p-1)] %= p
		if mods[0] == 0:
			ng = False
			for i in range(1, p-1):
				if mods[i] != 0:
					ng = True
					break
			if not ng:
				print(p)

Buggy submission (verdict: Runtime Error):
import sys
from math import sqrt
from math import gcd
n = int(input())
a = [int(input()) for _ in range(n+1)]
m = a[0]
for i in range(1, n+1):
	m = gcd(m, abs(a[i]))
ps = []

i = 2
while i**2 <= m:
#for i in range(2, int(sqrt(m))+1):
	if m%i == 0:
		ps.append(i)
		while m%i == 0:
			m //= i
	i += 1
if m != 1:
	ps.append(m)

prime = []
for i in range(2, n+1):
	for p in prime:
		if i%p == 0:
			break
	else:
		prime.append(i)

ps = sorted(list(set(ps + prime)))
if n == 0:
	if ps:
		print(*ps, sep="\n")
	sys.exit()
a = a[::-1]
for p in ps:
	if p-1 > n:
		ng = False
		for i in range(1, n+1):
			if a[i]%p != 0:
				ng = True
				break
		if not ng:
			print(p)
	else:
		mods = [0 for _ in range(p-1)]
		for i in range(1, n+1):
			mods[i%(p-1)] += a[i]
			mods[i%(p-1)] %= p
		if mods[0] == 0:
			ng = False
			for i in range(1, p-1):
				if mods[i] != 0:
					ng = True
					break
			if not ng:
				print(p)

Buggy submission (verdict: Runtime Error):
from sys import exit
from math import sqrt
n = int(input())
a = [int(input()) for _ in range(n+1)]
#xx = [0, 1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6]
x = 0
#for x in xx:
while True:
	m = abs(sum([a[i]*pow(x, n-i) for i in range(n+1)]))
	if m != 0:
		break
	x += 1
ps = []
for i in range(2, int(sqrt(m))+1):
	if m%i == 0:
		ps.append(i)
		while m%i == 0:
			m //= i
if m != 1:
	ps.append(m)
if n == 0:
	if ps:
		print(*ps, sep="\n")
	exit()
a = a[::-1]

Buggy submission (verdict: Runtime Error):
from sys import exit
from math import sqrt
n = int(input())
a = [int(input()) for _ in range(n+1)]
xx = [0, 1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6]
for x in xx:
	m = abs(sum([a[i]*pow(x, n-i) for i in range(n+1)]))
	if m != 0:
		break
	#x += 1
ps = []
for i in range(2, int(sqrt(m))+1):
	if m%i == 0:
		ps.append(i)
		while m%i == 0:
			m //= i
if m != 1:
	ps.append(m)
if n == 0:
	if ps:
		print(*ps, sep="\n")
	exit()
a = a[::-1]
print("WA")

Buggy submission (verdict: Runtime Error):
from sys import exit
from math import sqrt
n = int(input())
a = [int(input()) for _ in range(n+1)]
xx = [0, 1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6]
for x in xx:
	m = abs(sum([a[i]*pow(x, n-i) for i in range(n+1)]))
	if m != 0:
		break
	x += 1
ans, ps = [], []
for i in range(2, int(sqrt(m))+1):
	if m%i == 0:
		ps.append(i)
		while m%i == 0:
			m //= i
if m != 1:
	ps.append(m)
if n == 0:
	if ps:
		print(*ps, sep="\n")
	exit()
a = a[::-1]
for p in ps:
	if p-1 > n:
		ng = False
		for i in range(1, n+1):
			if a[i]%p != 0:
				ng = True
				break
		if not ng:
			print(p)
	else:
		mods = [0 for _ in range(p-1)]
		for i in range(1, n+1):
			mods[i%(p-1)] += a[i]
			mods[i%(p-1)] %= p
		if mods[0] == 0:
			ng = False
			for i in range(1, p-1):
				if mods[i] != 0:
					ng = True
					break
			if not ng:
				print(p)

Buggy submission (verdict: Runtime Error):
from sys import exit
from math import sqrt
n = int(input())
a = [int(input()) for _ in range(n+1)]
x = 0
while True:
	m = abs(sum([a[i]*pow(x, n-i) for i in range(n+1)]))
	if m != 0:
		break
	x += 1
ans, ps = [], []
for i in range(2, int(sqrt(m))+1):
	if m%i == 0:
		ps.append(i)
		while m%i == 0:
			m //= i
if m != 1:
	ps.append(m)
if n == 0:
	if ps:
		print(*ps, sep="\n")
	exit()
a = a[::-1]
for p in ps:
	if p-1 > n:
		ng = False
		for i in range(1, n+1):
			if a[i]%p != 0:
				ng = True
				break
		if not ng:
			print(p)
	else:
		mods = [0 for _ in range(p-1)]
		for i in range(1, n+1):
			mods[i%(p-1)] += a[i]
			mods[i%(p-1)] %= p
		if mods[0] == 0:
			ng = False
			for i in range(1, p-1):
				if mods[i] != 0:
					ng = True
					break
			if not ng:
				print(p)

Buggy submission (verdict: Runtime Error):
from sys import exit
from math import sqrt
n = int(input())
a = [int(input()) for _ in range(n+1)]
x = 0
while True:
	m = abs(sum([a[i]*pow(x, n-i) for i in range(n+1)]))
	if m != 0:
		break
	x += 1
if x > 0:
	m *= x
#print(m)
ans, ps = [], []
for i in range(2, int(sqrt(m))+1):
	if m%i == 0:
		ps.append(i)
		while m%i == 0:
			m //= i
if m != 1:
	ps.append(m)
if n == 0:
	if ps:
		print(*ps, sep="\n")
	exit()
a = a[::-1]
for p in ps:
	if p-1 > n:
		ng = False
		for i in range(1, n+1):
			if a[i]%p != 0:
				ng = True
				break
		if not ng:
			print(p)
	else:
		mods = [0 for _ in range(p-1)]
		for i in range(1, n+1):
			mods[i%(p-1)] += a[i]
			mods[i%(p-1)] %= p
		if mods[0] == 0:
			ng = False
			for i in range(1, p-1):
				if mods[i] != 0:
					ng = True
					break
			if not ng:
				print(p)

Buggy submission (verdict: Runtime Error):
from sys import exit
from math import sqrt
n = int(input())
a = [int(input()) for _ in range(n+1)]
if a[n] == 0:
	x = 1
else:
	x = 0
for i in range(n, -1, -1):
	if a[i] != 0:
		a = a[:i+1]
		n = i
		break
#print(a, n)
#m = abs(sum(a))
while True:
	m = abs(sum([a[i]*pow(x, n-i) for i in range(n+1)]))
	if m != 0:
		break
	x += 1
if x > 0:
	m *= x
#print(m)
ans, ps = [], []
for i in range(2, int(sqrt(m))+1):
	if m%i == 0:
		ps.append(i)
		while m%i == 0:
			m //= i
if m != 1:
	ps.append(m)
if n == 0:
	if ps:
		print(*ps, sep="\n")
	exit()
a = a[::-1]
for p in ps:
	if sum(a)%p == 0:
		print(p)

Buggy submission (verdict: Runtime Error):
from sys import exit
from math import sqrt
n = int(input())
a = [int(input()) for _ in range(n+1)]
m = abs(a[n])
ans, ps = [], []
for i in range(2, int(sqrt(m))+1):
	if m%i == 0:
		ps.append(i)
		while m%i == 0:
			m //= i
if m != 1:
	ps.append(m)
if n == 0:
	print(*ps, sep="\n")
	exit()
a = a[::-1]
for p in ps:
	if p-1 > n:
		ng = False
		for i in range(1, n+1):
			if a[i]%p != 0:
				ng = True
				break
		if not ng:
			print(p)
	else:
		mods = [0 for _ in range(p-1)]
		for i in range(1, n+1):
			mods[i%(p-1)] += a[i]
			mods[i%(p-1)] %= p
		if mods[0] == 0:
			ng = False
			for i in range(1, p-1):
				if mods[i] != 0:
					ng = True
					break
			if not ng:
				print(p)
		elif mods[0] == 1:
			ng = False
			for i in range(1, p-1):
				if mods[i] != 1:
					ng = True
					break
			if not ng:
				print(p)