Question

how i can prove 222221 is composite

Answer 1

222221 = 359 * 619

Since it has other factors also except 1 and the number itself, thus it is a composite number

Answer 2

@ikram002p try this when free...

Answer 3

one failed attempt :

222221 is NOT a prime if we could show that :
\[\large a^{222221 } \not \equiv a \mod 222221 \]

I have tried to reduce using a=2, 3... but its not simplifying :
\[\large 2^{222221 } \not \equiv 2 \mod 222221 \]

Answer 4

mm ganesh im not sure the inverse of frmats work mmm
how ever it has factorz mmm

Answer 5

fermats set if p is prime then
a^p= a mod p , but that does not means if there exist n such that

a^n=a mod n for any n then n should be prime :o

Answer 6

we can use contrapositive right ?

\(p\) is NOT a prime number if :
\[\large a^p \not \equiv a \mod p\]

for some \(a\)

Answer 7

yeah that works xD

Answer 8

we're not proving \(p\) is a prime number,
we're trying to prove \(p\) is NOT a prime number

Answer 9

I have tried a=2, 3 and gave up on this already... >.<

Answer 10

well lets try wilson :o

Answer 11

(p-1) ! =-1 mod p

Answer 12

Oh never used wilson for prime testing before xD

Answer 13

i think mmm we only need to check if
(222220 ) ! = -1 mod 222221

Answer 14

hehe but that sounds like more factorization xD

Answer 15

lets go back to FLT

Answer 16

yeah :P findint counter example

Answer 17

well i bet 359, 619 wont work , right ?

Answer 18

4 also dnt work :O

Answer 19

4 and 2 are same

Answer 20

3 also :o

Answer 21

well it does not work for 2,3,4,5,6 :P
thats enough right ?

Answer 22

yeah thats more than enough to give up :P

Answer 23

lolz ok u already set it up :P

Answer 24

then \(\huge\cal\color{pink}{^❤ _❤❤done_❤❤^❤_❤} \)

Answer 25

well 222221 is divisible by 359 so you can say it is composite