4529.sagews

(x0,x1,x2,x3,x4)=577,114,910,666,107

multiple1=(x3-x2)*(x1-x0)-(x2-x1)^2; multiple1

-520644

multiple2=(x4-x3)*(x2-x1)-(x3-x2)^2;multiple2

-504500

gcd(multiple1,multiple2)

4036

factor(4036)

2^2 * 1009

# The modulo is one of 1009, 2018 or 4036
# We first try 4036
m = 4036

# Compute the inverse of the factor (x_n-x_{n+1}) modulo m
inv=1/Mod(x0-x1,m); inv

1787

# We solve the system modulo m
(a,b)=(Mod( (x1-x2)*inv, m) , Mod( (-x1^2+x0*x2)*inv, m) );a,b

(2256, 2030)

# Check if the modulo was correct ?
a*x0+b,a*x1+b,a*x2+b,a*x3+b,a*x4+b

(114, 910, 666, 3134, 1262)

# The modulo is one of 1009, 2018 or 4036
# We now try 1009
m = 1009
inv=1/Mod(x0-x1,m)
(a,b)=(Mod( (x1-x2)*inv, m) , Mod( (-x1^2+x0*x2)*inv, m) );a,b

(238, 12)

# We have found the correct modulo and factors of the LCG
a*x0+b,a*x1+b,a*x2+b,a*x3+b,a*x4+b

(114, 910, 666, 107, 253)