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:
? can u take a pic of the question?
Step-by-step explanation:
I recommend using desmos graphing calculator. It helps me with my algebra homework. Especially with slope equations and etc..
Answer:
The answer to your question is: x = -1
Step-by-step explanation:
Data
slope of l = x
slope of m = x +2
they are ⊥
Process
If they are ⊥, then, x + 2 = - 1/x
x(x + 2) = -1
x² + 2x = -1
x² + 2x + 1 = 0
(x + 1)² = 0
x + 1 = 0
x = -1
