Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2013-05-18 23:00:49

johnathon bresly
Guest

sigma function

hi,can anyone help me with this-
find one n such that

(if any) also please tell me how you found it for my better understanding.

#2 2013-05-19 00:28:19

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: sigma function

What does sigma mean over here?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

#3 2013-05-19 02:26:53

Johnathon bresly
Guest

Re: sigma function

Sigma function is the function that produces the sum of a integer's positive divisors.example:

.

#4 2013-05-19 02:46:11

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: sigma function

I am guessing such a solution does not exist.

I will bring up a proof


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

#5 2013-05-19 03:14:53

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: sigma function

Consider the factors of n to be

and the sum of
be x.
Consider the factors of n+1 to be
and the sum of
be x-1.

There must be exactly one

for which another
have the relation
.
Therefore, all the rest factors are common.
But, since gcd(n, n+1) =1, therefore, no other common factor other than 1 can exist.
Thus, there are only three factors.

Now, let us imagine that the factors of the first number are 1, a and n and the second number are 1, a-1, n+1
But, whenever there are just three factors of a number, they are perfect squares.
But, two positve perfect squares cannot be consecutive. So no such number exists


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

#6 2013-05-19 15:37:35

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: sigma function

I am sorry. This proof seems to be seriously flawed


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

#7 2013-05-19 17:52:24

{7/3}
Member
Registered: 2013-02-11
Posts: 210

Re: sigma function

Hi,johnathon bresly,do you know the formula

Last edited by {7/3} (2013-05-19 17:53:57)


There are 10 kinds of people in the world,people who understand binary and people who don't.

Offline

#8 2013-05-19 17:54:11

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,665

Re: sigma function

Hi {7/3}

How does that help?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#9 2013-05-19 18:40:54

{7/3}
Member
Registered: 2013-02-11
Posts: 210

Re: sigma function

Well, n and n+1 don't have any common primes,which can be a starting point


There are 10 kinds of people in the world,people who understand binary and people who don't.

Offline

#10 2013-05-20 00:39:18

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,665

Re: sigma function

Yes, but there are many other cases to consider.

And, sorry if the last post sounded rude.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#11 2013-05-20 03:47:28

{7/3}
Member
Registered: 2013-02-11
Posts: 210

Re: sigma function

It's okay,and i know there are many other cases but i wanted to give johnathon some facts so that he can make a strategy and solve it himself


There are 10 kinds of people in the world,people who understand binary and people who don't.

Offline

Board footer

Powered by FluxBB