How can i Prove that 10 is a solitary number?

Question

tanya123 · Answer

Have you proved it yet?

anonymous · Answer

nope

anonymous · Answer

It's a simple question thus so hard

tanya123 · Answer

Solitary numbers have positive density, disproving a conjecture

anonymous · Answer

attachment

anonymous · Answer

i know but the important thing is what proves that 10 has a positive density and a disproving a conjecture

tanya123 · Answer

10 is not a power of a prime, nor is it prime itself.
This means that in order to prove that it is indeed solitary, it must be disproved that it is friendly, or we must find a way to prove a number as being solitary.

tanya123 · Answer

@ganeshie8

anonymous · Answer

hmm

ganeshie8 · Answer

show that  $\large   \gcd(10, \sigma (10))  \ne 1$

anonymous · Answer

What kind of math is this btw?

ganeshie8 · Answer

divisors of 10 :  {1, 2, 5, 10}

$\large \sigma(10) =   1+2+5+10 =  18$

$\large \gcd(10, 18) = 2 \ne 1$ 
so 10 is not a solitary number

ganeshie8 · Answer

number theory

ganeshie8 · Answer

seems i have misinterpreted the definition of solitary number http://www.mathsisgoodforyou.com/conjecturestheorems/10solitary.htm

anonymous · Answer

guys if it's hard just give up on it

anonymous · Answer

no need to fry your brain for me

ganeshie8 · Answer

$\large   \gcd(10, \sigma (10))  = 1$ is a necessary condition for solitary numbers, not a sufficient condition hmm

anonymous · Answer

time to close this and end it for all

anonymous · Answer

fry you brain lol

mrnood · Answer

This is a quote from Wikipedia (NOT my own knowledge):


No general method is known for determining whether a number is friendly or solitary. The smallest number whose classification is unknown (as of 2009) is 10; it is conjectured to be solitary; if not, its smallest friend is a fairly large number.