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 smallest unit of measure is the millimeter
Hope this helps ;)
Remember, mean is average. So first you add them all up, and then divide by the total number. All the dollars added up and then divided by 6 equals 59. So, working backwards, if you multiply 6 (the number of categories) by 59 you get the total of all money earned from every category. 6 times 59 equals 354. But if you add what you can see right now, it only equals 274. So the t-shirt total must be the difference between the two... 80 dollars.
Answer:
21 roses
Step-by-step explanation:
49 / 7 = 7
Each friend got 7 roses.
7 x 3 = 21
3 friends combine their roses together, making a bouquet of 21 roses.
Answer:
the answer would be 2/5
Step-by-step explanation:
you add up all of the boys to get 8
there are, in total 20 students that can be chosen, so there is an 8/20 chance that it would be a boy, simplified that is 2/5
