Answer:
Check the explanation
Step-by-step explanation:
(a)Let p be the smallest prime divisor of (n!)^2+1 if p<=n then p|n! Hence p can not divide (n!)^2+1. Hence p>n
(b) (n!)^2=-1 mod p now by format theorem (n!)^(p-1)= 1 mod p ( as p doesn't divide (n!)^2)
Hence (-1)^(p-1)/2= 1 mod p hence [ as p-1/2 is an integer] and hence( p-1)/2 is even number hence p is of the form 4k+1
(C) now let p be the largest prime of the form 4k+1 consider x= (p!)^2+1 . Let q be the smallest prime dividing x . By the previous exercises q> p and q is also of the form 4k+1 hence contradiction. Hence P_1 is infinite
The correct answer is 25.12 cubic inches
Answer:
x=12
Step-by-step explanation:
First you make sure x is on both sides of the equation. So you do 0.7x-5-0.2x=0.2x+1-0.2x. Which just simplifies to 0.5x-5=1. You make sure x is the only thing on that side of the equation so you do 0.5x-5+5=1+5 which simplifies to 0.5x=6. Multiply the equation times 2 to just have x. x=12. The value that makes true of x is 12.
I dont know the awnser sorry
