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:
12,132
Step-by-step explanation:
It says a restaurant chain bakes 6,777 more key lime pies that cocunut cream pies. This means regardless of the amount of cream pies, the restaurant chain bakes 6,777 more.
So....
5,355+6,777 = 12,132
Answer:
Step-by-step explanation:
It is two types of function.
- Exponential Growth: If function increase as value of x increase.
In this case, a>0 and b>1
- Exponential decay: If function decrease as value of x increase.
In this case, a>0 and 0<b<1
We need to choose exponential growth function.
Here a=0.75>0 and b=5>1
Therefore, This function is exponential growth.
Answer:
264,666.
Step-by-step explanation:
We have been given that a number has seven digits.
All digits are 6 except the hundred-thousands' digit.
Hundred thousands: 100,000.
The hundred thousand's digit is 2, so its value would be 200,000.
We have been given that thousands's digit is 4, so its value would be:
4 thousands: 4,000
The number with given hundred thousand's and thousands's digit would be 204,000.
Since all digits are 6 except the hundred-thousands' digit, therefore, our number would be 264,666.
The correct answer to your problem is 96
