######################################
p1=10151
x1=-6144%p1
p2=10079
x2=-3742%p2
x=x2-x1
R=IntegerModRing(p2)
y=(R(p1)^-1)*(x)
R2=IntegerModRing(p1*p2)
Y=R2(y)
X=x1+(p1*Y)
print "x =",x1,"+",p1,"y"
print "x =",x1,"+",p1,"y =",x2,"(mod",p2,")"
print "y =",p1,"^-1*",x,"(mod",p2,")"
print "y =",p1,"^-1*",x%p2,"(mod",p2,")"
print "y =",Y,"(mod ",p2,")"
print "x =",x1,"+",p1,"*",y,"=",X,"(mod",p1*p2,")"
######################################
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x = 4007 + 10151 y
x = 4007 + 10151 y = 6337 (mod 10079 )
y = 10151 ^-1* 2330 (mod 10079 )
y = 10151 ^-1* 2330 (mod 10079 )
y = 3672 (mod 10079 )
x = 4007 + 10151 * 3672 = 37278479 (mod 102311929 )
x = 4007 + 10151 y
x = 4007 + 10151 y = 6337 (mod 10079 )
y = 10151 ^-1* 2330 (mod 10079 )
y = 10151 ^-1* 2330 (mod 10079 )
y = 3672 (mod 10079 )
x = 4007 + 10151 * 3672 = 37278479 (mod 102311929 )
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