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
Answer:
the formula is a_n = 6n - 5
Step-by-step explanation:
The formula is
Given that
{1, 7, 13, 19, 25, . . . }
The difference between the numbers is
7 - 1 = 6
13 -7 = 6
19 - 13 = 6
a = 1
d = 6
Now the formula is
a_n = a + (n - 1)d
= 1 + (n - 1)6
= 1 + 6n - 6
= 6n - 5
So, the formula is a_n = 6n - 5
The answer is 4 because if u divide both equations by eachother you get 4
Answer:
The area is 300 ft².
Step-by-step explanation:
The formula for the area of a parallelogram is A=bh. The base is 20, the height is 15, 20×15 is 300ft².
pretty sure...
Answer:
root x-3 _> 0 is correct
Step-by-step explanation:
