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
Given:
The line passing through (-2,5) and (2,p) has a gradient of 
.
To find:
The value of p.
Solution:
If a line passes through two points, then the slope of the line is:
The line passing through (-2,5) and (2,p). So, the slope of the line is:
It is given that the gradient or slope of the line is .
On cross multiplication, we get
Divide both sides by 2.
Therefore, the value of p is 3.
Answer:
future: a day, a week, or even a few months from now.
short-term goal
long-term goal
intermediate goal
specific goa
Step-by-step explanation:
please mark me as brainliest hi
Answer:x=3
Step-by-step explanation:
Add 4 to both sides and get 3x=5+4
Simplify 5+4 to 9 and get 3x=9
Divide both sides by 3 and get x=9/3
Simplify 9/3 to 3 and get the answer x=3
Across the y axis. This question becomes easier if you graph it out in your head. Let's say the bank is at (2,2). Because the grocery store has an opposite x coordinate, the bank would be at (-2,2). If you look at this in your head, they are not even on different sides of the x axis, and therefore must be reflected across the y axis.
