Question-1763

Question Number 1763 by Gerlândio Almeida last updated on 18/Sep/15

Commented by 123456 last updated on 18/Sep/15

p_{0} (n) = x n

r (n) = α x n

p_{1} (n) = p_{0} (n) - r (n) = (1 - α) x n

r (n) ⩾ p_{0} (m)

α x n ⩾ x m x > 0

n ⩾ \frac{m}{α} α > 0

p_{0} (n) ⩾ \frac{x m}{α}

r_{0} (n) ⩾ x m

p_{1} (n) ⩾ \frac{(1 - α) x m}{α}

(n, m) \in Z^{2}

α ∖ m 1 2 3 4 5

0, 20 5 10 15 20 25

0, 35 3 6 9 12 15

0, 50 2 4 6 8 10

Answered by 123456 last updated on 18/Sep/15

\underset{n = 0}{\sum^{\infty}} x^{n} = \frac{1}{1 - x}

\prod_{p \in P} \frac{1}{1 - p^{- s}} = \prod_{p \in P} \underset{n = 0}{\sum^{\infty}} p^{- s n} = \underset{n = 1}{\sum^{\infty}} n^{- s}, s > 1

Facebook Tweet Pin