[SWPU 2020]happy

题目：

('c=', '0x7a7e031f14f6b6c3292d11a41161d2491ce8bcdc67ef1baa9eL')
('e=', '0x872a335')
#q + q*p^3 =1285367317452089980789441829580397855321901891350429414413655782431779727560841427444135440068248152908241981758331600586
#qp + q *p^2 = 1109691832903289208389283296592510864729403914873734836011311325874120780079555500202475594

解题：

q+q*p^3=s1
q*p+q*p^2=s2

q*(1+p^3)=s1->q*(1+p)*(p^2-p+1)=s1
q*p*(1+p)=s2

q*(1+p)=gmpy2.gcd(s1,s2)

p=s2//gmpy2.gcd(s1,s2)
q=gmpy2.gcd(s1,s2)//(1+p)
print("p =",p)
print("q =",q)
#p = 1158310153629932205401500375817
#q = 827089796345539312201480770649

import gmpy2
from Crypto.Util.number import *

c = 0x7a7e031f14f6b6c3292d11a41161d2491ce8bcdc67ef1baa9e
e = 0x872a335
q = 827089796345539312201480770649
p = 1158310153629932205401500375817
n = p*q
d = gmpy2.invert(e,(p-1)*(q-1))
m = pow(c,d,n)
print(long_to_bytes(m))

解得：flag{happy_rsa_1}