On the Number of Prime Factors of a Finite
نویسندگان
چکیده
contributions to Catalan's classical problem to show that 8,9 is the only pair of consecutive positive integers which are both perfect powers. The work of Professor Ko and the related work by others show that there is just one mathematical world and that there are no borders in this world. For any positive integer n let P (n); !(n); (n) denote the greatest prime factor of n, the number of distinct prime factors of n, the number of prime numbers not exceeding n, respectively. Put P (1) = 1; !(1) = 0: Let a; d; k be positive integers with gcd(a; d) = 1: Put = a(a + d) : : : (a + (k ? 1)d): in 1892 Sylvester 7] proved that a d + k implies (1) P (() > k:
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