Legendre's Formula
Автор: sumchief
Загружено: 2022-08-04
Просмотров: 2470
Описание:
this video discusses Legendre's formula , which is a summation for the exponent of the largest power of a prime p that divides the factorial n!. It is also known as de Polignac's formula .
For any prime number p and any positive integer n, the exponent of the largest power of p that divides n (that is, the p-adic valuation of n) uses the floor function .
While the formula on the right side is an infinite sum, for any particular values of n and p it has only finitely many nonzero terms and infinitely 0 terms .
also we can reformulate Legendre's formula in terms of the base-p expansion of n. s subscript p of n denote the sum of the digits in the base-p expansion of n .
In number theory, the p-adic valuation or p-adic order of an integer n is the exponent of the prime number p that divides n.
#legendre
#numbertheory
#numbersystem
#primefactors
#primenumbers
#prime
#algebra
#calculus
#calcio
#calciatori #sumchief
#somesums
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