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We prove that every natural number greater than 1 can be factorized into a sequence of prime numbers, i.e.,

We proceed by complete induction over

forallninN:n> 1 =>( existskinN,f:N_{k}->N:n= (prod_{0 <= i < k}f(i)) /\foralliinN_{k}:f(i) is prime).

We take arbitrary `n` in **N** and assume

We have to show

(1) forallm<n:m> 1 =>( existskinN,f:N_{k}->N:m= (prod_{0 <= i < k}f(i)) /\foralliinN_{k}:f(i) is prime).

n> 1 =>( existskinN,f:N_{k}->N:n= (prod_{0 <= i < k}f(i)) /\foralliinN_{k}:f(i) is prime).

*See lecture notes.*

Author: Wolfgang Schreiner

Last Modification: November 24, 1999