A secure LCG?
70 points Hard

My friend has lately told me that he's implemented a Pseudorandom Number Generator.

It sounded pretty cool, apart from the fact that he's always been a script kiddie...

He gave me some additional info and wanted to see if it was possible to predict the next number based on the 3 previous numbers.

Additional info:

PRNG is based on "LCG", https://en.wikipedia.org/wiki/Linear_congruential_generator;
    Meaning: x_n+1 = (a*x_n + c) mod m

Generated numbers are natural numbers;

Biggest possibly generated value is: 121409833232633162280;

He chose "special values" for "a" and "c", so that "it's harder to break it";

The following numbers were generated sequentially:

x1 = 65001687610455615650

x2 = 880901038222735

x3 = 16032398895653777

I think I've tried already every "LCG breaker" tool out there on the internet, but none of them has happened to work (each threw some strange error).

Would you please help me?

P.S.

The flag format is: CTFlearn{ASCII representation of the predicted number}

E.g. predicted number = 84698384, then the flag is: CTFlearn{TEST} (84 => "T", 69 => "E"...)

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Rating 4.77
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Discussion

hey fellas, you can go from here: https://www.youtube.com/watch?v=UBSUTidDJbU

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damn, i should take a rest

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Don't be afraid by this one: should be rated as easy / medium (category: maths)

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it's all about math and modulus equation

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I would love to see how others solved it. My method is pretty dirty ;)

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Hey! Check your discord dm. I sent you the intended way to solve this challenge :)

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I need the method

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I need the method

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