1) Venn-diagram of-<br> AUBUC={a,b,c,d,e}U{d,e,f,g,h,i}U{a,e,i,o,u}<br>
Naddika [18.5K]
Answer:
AUBUC= { a,b,c,d,e,f,g,h,i,o,u}
Answer:
yes
Step-by-step explanation:
indeed
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
