q- – Tinku Tara

Question Number 5772 by sagarvijay444@gmail.com last updated on 27/May/16

q +

Commented by FilupSmith last updated on 27/May/16

\exists x \in Z^{+} : x = p q, p, q \in Z^{+} ∖ {0, 1}

n, i \in P

p = \prod_{n ∣ p} n

q = \prod_{i ∣ q} i

∴ x = product of factors of p and q

if p = a_{1} \times a_{2} \times \dots \times a_{n}

q = b_{1} \times b_{2} \times \dots \times b_{i}

x = (a_{1} \times \dots \times a_{n}) (b_{1} \times \dots \times b_{i})

x = (a_{1} \times \dots \times a_{n} \times b_{1}) (b_{2} \times \dots \times b_{i})

x = (a_{2} \times \dots \times a_{n}) (a_{1} \times b_{1} \times \dots \times b_{i})

e t c

You can't use 'macro parameter character #' in math mode

= (n + i)!

e . g .

x = 12

= 2 \times 6

= 2 \times 2 \times 3

You can't use 'macro parameter character #' in math mode

x_{1} = 2 \times 2 \times 3 = 2 \times 6

x_{2} = 2 \times 2 \times 3 = 4 \times 6

x_{3} = 2 \times 2 \times 3 = 6 \times 2

(later half is reverse a b = b a)

x_{4} = 6 \times 2

x_{5} = 6 \times 4

x_{6} = 2 \times 6

∴ number of ways to multiply two

numbers to get any + ve integer x

is equal to the factorial of the number of

prime factors x has .

(e x c l u d i n g a = 1 a = a 1)

i . e . p, q \neq 1

\bar{} \bar{} ∖ (° ⌣ °) / \bar{} \bar{}

q-