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
Should be 55 because they are inversely with x
Answer:
1.62,15/20,16.2%
Step-by-step explanation:
Answer: 682
Also, each rectangle’s width is half its height. It can be expressed as
w= 1/2h<span>
The first rectangle is 32cm tall. Then the measurement would be
h=32
w= 1/2h= 16
</span>The first rectangle is 32cm tall and e<span>ach rectangle is half as tall as the previous one. That can be expressed as
h(n)= 32(1/2)^n-1
The area of rectangle is
area(n)= h*w
area(n)=h*</span> (1/2h)= 1/2h ^2
area(n)= 1/2 {32(1/2)^n-1}^2<span>
area(n)= 512(1/2)^2n-2
Then the sum of the 5 rectangle would be:
</span>area(1) + area(2) + area(3) + area(4)+ area(5)
512(1/2)^2(1)-2 + 512(1/2)^2(2)-2 + 512(1/2)^2(3)-2 + 512(1/2)^2(4)-2 +512(1/2)^2(5)-2 =
512+ 512/4 + 512/16+ 512/ 64 + 512/ 256=
512+ 128 + 32+ 8 + 2= 682
