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 amount of money she spends per year on utility bills for the air conditioner is; D: $176.40
<h3>How to solve algebra word problems? </h3>
We are told that;
Cost of running the air conditioner = 7 hours per day
Cost of running the air conditioner = 21 cents per hour = $0.21 per hr.
She runs it for four months at 7 hours per day. Thus;
Total number of hours for the 4 months = 7 × 30 × 4 = 840 hours
Total cost for the 4 months = $0.21 per hr. × 840 hours = $176.4
Read more about algebra word problems at; brainly.com/question/21405634
<span>3 + ((-5) + 6) = (3 + (-5)) + 6
It's </span>associative property of addition
The associative property of addition states that you can add regardless of how the numbers are grouped, result will state the same.
5x + 2 is a denominator.
A denominator cannot equal zero since division by zero is undefined.
Set the denominator equal to zero and solve for x to find which value of x makes the denominator zero.
5x + 2 = 0
5x = -2
x = -2/5
The non-permissible replacement for the variable is -2/5.
