package euler

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package euler

euler
- Euler
  - Arith
    
    Unsafe
  - Diophantine
  - Farey
  - Modular
    
    Make
    
    _
  - Primes

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Solving diophantine equations, i.e. equations on integers.

exception No_solution

Raised when a system has no solution.

val solve_congruences : (int * int * int) Stdlib.Seq.t -> int * int

solve_congruences @@ List.to_seq [ (a1, b1, m1) ; … ; (ak, bk, mk) ], provided that the m_i are non-zero, solves the following linear congruence system of unknown x:

a₁ · x ≡_m₁ b₁
…
a_k · x ≡_{m_k} b_k

TODO: complexity?

returns
a pair (x, m) where 0 ≤ x < m, which represents the set of solutions x + mℤ,

raises No_solution
if there are no solutions.