Fibonacci Numbers
نویسنده
چکیده
One can prove the following three propositions: (1) For all natural numbers m, n holds gcd(m,n) = gcd(m, n + m). (2) For all natural numbers k, m, n such that gcd(k, m) = 1 holds gcd(k,m · n) = gcd(k, n). (3) For every real number s such that s > 0 there exists a natural number n such that n > 0 and 0 < 1 n and 1 n ¬ s. In this article we present several logical schemes. The scheme Fib Ind concerns a unary predicate P, and states that: For every natural number k holds P[k] provided the following conditions are met: • P[0], • P[1], and • For every natural number k such that P[k] and P[k + 1] holds P[k + 2].
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