EQUATIONS AND INEQUALITIES INVOLVING vp(n!)
نویسنده
چکیده
In this paper we study vp(n!), the greatest power of prime p in factorization of n!. We find some lower and upper bounds for vp(n!), and we show that vp(n!) = n p−1 + O(lnn). By using the afore mentioned bounds, we study the equation vp(n!) = v for a fixed positive integer v. Also, we study the triangle inequality about vp(n!), and show that the inequality pp > qq holds for primes p < q and sufficiently large values of n.
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