Proof by induction of the strong Goldbach's conjecture
Résumé
To prove the conjecture, we consider for any even natural number 2n > 4, with n > 2, the finite sequence of natural numbers Sm (n) = (si (n)) defined by : si (n) = 2n-pi, with i belonging to set {1,2,...,m}, where pi is the i-th prime number in the finite strictly ordered sequence of primes Pm := p1 = 2 < p2 = 3 < p3 = 5 < ... < pm, where m denotes the number of primes p such that p < 2n. Using two stages of proofs: the proof by contradiction and mathematical induction, we prove that, for any natural number n > 2, there exists at least one prime number sr (n) = 2n - pr belonging to the sequence Sm (n), which confirms the result 2n = sr (n) + pr where pr is the r-th prime number of the sequence Pm . This result attests the validity of Goldbach's statement which expresses that: every even integer 2n > 4, with n> 2, is the sum of two primes.
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