Tags: polynomial crypto
Since there are at most 50 requests, it is a reasonable assumption that the degree of the polynomial is at most 49.
But to illustrate the solution, let us say we only have a quadratic polynomial
f(x) = a + bx + cx^2
The if we evaluate `f(x1)` we get,
f(x1) = a + b*(x1) + c*(x1^2)
We can evaluate `f(.)` several times to get a system of linear equations, and solve for the coefficients.
f(0) = 2
f(1) = 39
f(2) = 99
2 = a + 0b + 0c
39 = a + 39b + 1521c
99 = a + 99b + 9802c
This can be solved this using gaussian elimination, and we extend this to polynomial degree 49, and the coefficients of the polynomial represent the flag
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