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:
200
Step-by-step explanation:
Jack share = 2/5 x 1/5 = 2/25
amount left over = 1 - (2/25 + 2/5) = 13/25
13/25 x t = 260
t = total amount of chocolate
t = (260 x 25) / 13 = 500
Davids share = 2/5 x 500 = 200
Answer: 79
Step-by-step explanation:
Line up the numbers from least to greatest. 39, 42, 44, 51, 55, 62, 66, 72, 77, 81, 94, 86 Then find the Median. Look at the upper part of the data set and from there find the 3rd quartile.
69.1 is already a decimal.
Answer:
The distributive property tells us how to solve expressions in the form of a(b + c). The distributive property is sometimes called the distributive law of multiplication and division.
Step-by-step explanation:
