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Old 2021-05-11, 17:36   #2
Alberico Lepore
 
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May 2017
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@CRGreathouse your number
https://mersenneforum.org/showthread.php?t=25929


390644893234047643

sqrt(390644893234047643/2)=441692991 -> 441692991 ; 441692989 ;441692987 ; 441692985
sqrt(390644893234047643) =625015914 -> 625015913 ; 625015911 ;625015909 ; 625015907


(390644893234047643-3)/8-Q-[4-(441692985-7)*(441692985-5)/8]=441692985*X

(390644893234047643-3)/8-P-[4-(625015907-7)*(625015907-5)/8]=625015907*X

Q=441692985*x+152029391

P=625015907*y+60099037

p*(q-625015907)/8=625015907*y+60099037 ,p*q=390644893234047643

p=625015921-8*y

q*(p-441692985)/8=441692985*x+152029391,p*q=390644893234047643

q=884426299- 8*x





Use LLL alghorithm to find one solution of

m*(a1)*(a3)+n*(b1)*(b3) = N*t +T

m*(a1)*(a4)-n*(b1)*(b4) = N*s + S

m*(a2)*(a3)-n*(b2)*(b3) = N*w + W

64 < T <= 64 *j where j is integer > 1

0<S <= sqrt(N)

0<W <= sqrt(N)

a1=441692985 , a2=152029391 ,a3=625015907 ,a4=60099037

b1=8 , b2=884426299 , b3=8 , b4=625015921
Attached Files
File Type: pdf Lepore_Factorization_nr_88.pdf (58.8 KB, 124 views)

Last fiddled with by Alberico Lepore on 2021-05-18 at 10:27
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