Login

Search the forums now!

Welcome, Guest. Please login or register.

October 14, 2025, 03:15:21 am
Pages: [1] 2   Go Down

Author Topic: proof by contradiction? or other method?  (Read 6883 times)  Share 

0 Members and 1 Guest are viewing this topic.

Martoman

  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1476
  • Respect: +11
proof by contradiction? or other method?
« on: April 08, 2010, 03:32:54 am »
0
Show that is composite for all n when n is an integer.

Just a verification required

Assume is prime. Then some prime p,

which means

This however means that as the only prime number to divide 4 in such a way that it produces an integer answer... because you can't have a composite or prime decimal as far as I know. Having p restricted in such a way, means that the will be a fraction for some n (try n = 1) then isn't a natural number. Hence, a contradiction is reached assuming that it was prime to start with.
Hence, it must be composite.

*edit* 1...is..not...a...prime....number....

*edit twice, mainly because you dont_need_to_factorise... i factorized for whatever reason (ie: it was cool to do so)*
« Last Edit: April 08, 2010, 10:28:57 am by Martoman »
Logged
2009: Math methods: 50, Psychology: 44
2010: chem 47, further 48, Spesh 49 fml seriously and other yr 11 subs.
2011: Holidaying, screw school.
No. Not azn.
___________________________________
Swedish meal time all the time

brightsky

  • Victorian
  • ATAR Notes Legend
  • *******
  • Posts: 3136
  • Respect: +200
Re: proof by contradiction? or other method?
« Reply #1 on: April 08, 2010, 12:32:26 pm »
0
Wouldn't it be easier if you just factorised it?

.

Hence, it is a composite number.
Logged
2020 - 2021: Master of Public Health, The University of Sydney
2017 - 2020: Doctor of Medicine, The University of Melbourne
2014 - 2016: Bachelor of Biomedicine, The University of Melbourne
2013 ATAR: 99.95

Currently selling copies of the VCE Chinese Exam Revision Book and UMEP Maths Exam Revision Book, and accepting students for Maths Methods and Specialist Maths Tutoring in 2020!

the.watchman

  • Victorian
  • ATAR Notes Superstar
  • ******
  • Posts: 2526
  • Respect: +10
Re: proof by contradiction? or other method?
« Reply #2 on: April 08, 2010, 12:49:28 pm »
0
It may be worth noting that when solving the simultaneous equations:

AND

This does not yield integer solutions (nor does the opposite), thus suggesting that the factors cannot ONLY be 1 or itself when n is an integer

But proof by contradiction is way cooler 8-)
« Last Edit: April 08, 2010, 01:01:33 pm by the.watchman »
Logged
Remember, remember the 5th of November

2010 - MM CAS (47) - Cisco 1+2 (pass :P)
2011 - Eng - Phys - Chem - Spesh - Latin - UMAT
ATAR - 99.00+ plz... :)

Feel free to PM me for anything :D

brightsky

  • Victorian
  • ATAR Notes Legend
  • *******
  • Posts: 3136
  • Respect: +200
Re: proof by contradiction? or other method?
« Reply #3 on: April 08, 2010, 12:59:42 pm »
0
Why can't it be?

.
Logged
2020 - 2021: Master of Public Health, The University of Sydney
2017 - 2020: Doctor of Medicine, The University of Melbourne
2014 - 2016: Bachelor of Biomedicine, The University of Melbourne
2013 ATAR: 99.95

Currently selling copies of the VCE Chinese Exam Revision Book and UMEP Maths Exam Revision Book, and accepting students for Maths Methods and Specialist Maths Tutoring in 2020!

Martoman

  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1476
  • Respect: +11
Re: proof by contradiction? or other method?
« Reply #4 on: April 08, 2010, 01:00:07 pm »
0
Quote from: brightsky on April 08, 2010, 12:32:26 pm
Wouldn't it be easier if you just factorised it?

.

Hence, it is a composite number.

mmm see this is me not thinking what a prime number is. My argument works, although I like brightsky's as well.
Logged
2009: Math methods: 50, Psychology: 44
2010: chem 47, further 48, Spesh 49 fml seriously and other yr 11 subs.
2011: Holidaying, screw school.
No. Not azn.
___________________________________
Swedish meal time all the time

the.watchman

  • Victorian
  • ATAR Notes Superstar
  • ******
  • Posts: 2526
  • Respect: +10
Re: proof by contradiction? or other method?
« Reply #5 on: April 08, 2010, 01:01:17 pm »
0
Quote from: brightsky on April 08, 2010, 12:59:42 pm
Why can't it be?

.

I meant cannot ONLY be, sorry for confusion :P
Logged
Remember, remember the 5th of November

2010 - MM CAS (47) - Cisco 1+2 (pass :P)
2011 - Eng - Phys - Chem - Spesh - Latin - UMAT
ATAR - 99.00+ plz... :)

Feel free to PM me for anything :D

brightsky

  • Victorian
  • ATAR Notes Legend
  • *******
  • Posts: 3136
  • Respect: +200
Re: proof by contradiction? or other method?
« Reply #6 on: April 08, 2010, 01:04:00 pm »
0
Quote from: the.watchman on April 08, 2010, 01:01:17 pm
Quote from: brightsky on April 08, 2010, 12:59:42 pm
Why can't it be?

.

I meant cannot ONLY be, sorry for confusion :P

Ahh, gotcha. ;D
Logged
2020 - 2021: Master of Public Health, The University of Sydney
2017 - 2020: Doctor of Medicine, The University of Melbourne
2014 - 2016: Bachelor of Biomedicine, The University of Melbourne
2013 ATAR: 99.95

Currently selling copies of the VCE Chinese Exam Revision Book and UMEP Maths Exam Revision Book, and accepting students for Maths Methods and Specialist Maths Tutoring in 2020!

the.watchman

  • Victorian
  • ATAR Notes Superstar
  • ******
  • Posts: 2526
  • Respect: +10
Re: proof by contradiction? or other method?
« Reply #7 on: April 08, 2010, 01:10:54 pm »
0
Quote from: AzureBlue on April 08, 2010, 01:05:53 pm
Quote from: the.watchman on April 08, 2010, 12:49:28 pm
But proof by contradiction is way cooler 8-)
+1

Lol :)
Anyone got any good resources where I can get questions to practice? Or induction questions :)
Logged
Remember, remember the 5th of November

2010 - MM CAS (47) - Cisco 1+2 (pass :P)
2011 - Eng - Phys - Chem - Spesh - Latin - UMAT
ATAR - 99.00+ plz... :)

Feel free to PM me for anything :D

Martoman

  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1476
  • Respect: +11
Re: proof by contradiction? or other method?
« Reply #8 on: April 08, 2010, 01:15:17 pm »
0
Yes the art and craft of problem solving. I'm working through this now thanks to true tears. It has some really nice questions in it.

and err, is my proof right??? No one has answered this?

*edit* not to double post
Logged
2009: Math methods: 50, Psychology: 44
2010: chem 47, further 48, Spesh 49 fml seriously and other yr 11 subs.
2011: Holidaying, screw school.
No. Not azn.
___________________________________
Swedish meal time all the time

the.watchman

  • Victorian
  • ATAR Notes Superstar
  • ******
  • Posts: 2526
  • Respect: +10
Re: proof by contradiction? or other method?
« Reply #9 on: April 08, 2010, 01:19:01 pm »
0
Quote from: Martoman on April 08, 2010, 01:15:17 pm
Yes the art and craft of problem solving. I'm working through this now thanks to true tears. It has some really nice questions in it.

Good, I shall find this and try it. :)
Logged
Remember, remember the 5th of November

2010 - MM CAS (47) - Cisco 1+2 (pass :P)
2011 - Eng - Phys - Chem - Spesh - Latin - UMAT
ATAR - 99.00+ plz... :)

Feel free to PM me for anything :D

Martoman

  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1476
  • Respect: +11
Re: proof by contradiction? or other method?
« Reply #10 on: April 08, 2010, 01:20:36 pm »
0
TST = team selection tests for IMO?
..... epic.
Logged
2009: Math methods: 50, Psychology: 44
2010: chem 47, further 48, Spesh 49 fml seriously and other yr 11 subs.
2011: Holidaying, screw school.
No. Not azn.
___________________________________
Swedish meal time all the time

GerrySly

  • Victorian
  • Forum Leader
  • ****
  • Posts: 790
  • Respect: +5
Re: proof by contradiction? or other method?
« Reply #11 on: April 08, 2010, 01:27:07 pm »
0
Quote from: Martoman on April 08, 2010, 01:20:36 pm
TST = team selection tests for IMO?
..... epic.

You working to the IMO or just fulfilling a craving for maths?
Logged
VCE 2009
English, Methods, Specialist, IT: Software Development, Religion & Society, French

GerrySly

  • Victorian
  • Forum Leader
  • ****
  • Posts: 790
  • Respect: +5
Re: proof by contradiction? or other method?
« Reply #12 on: April 08, 2010, 01:45:21 pm »
0
The question was actually directed at Martoman, I know you are going for the IMO most of your posts are about getting there lol
Logged
VCE 2009
English, Methods, Specialist, IT: Software Development, Religion & Society, French

humph

  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1437
  • Respect: +16
Re: proof by contradiction? or other method?
« Reply #13 on: April 08, 2010, 02:13:21 pm »
0
Quote from: the.watchman on April 08, 2010, 12:49:28 pm
But proof by contradiction is way cooler 8-)
DISAGREE

Half the time it's not necessary anyway (as in this case) and can just lead to confusion.
See Tim Gowers' thoughts:
http://gowers.wordpress.com/2010/03/28/when-is-proof-by-contradiction-necessary/
Logged
VCE 2006
PhB (Hons) (Sc), ANU, 2007-2010
MPhil, ANU, 2011-2012
PhD, Princeton, 2012-2017
Research Associate, University College London, 2017-2020
Assistant Professor, University of Virginia, 2020-

Feel free to ask me about (advanced) mathematics.

the.watchman

  • Victorian
  • ATAR Notes Superstar
  • ******
  • Posts: 2526
  • Respect: +10
Re: proof by contradiction? or other method?
« Reply #14 on: April 08, 2010, 02:16:46 pm »
0
Ok, I get your point, but I've just learnt them recently :P
Logged
Remember, remember the 5th of November

2010 - MM CAS (47) - Cisco 1+2 (pass :P)
2011 - Eng - Phys - Chem - Spesh - Latin - UMAT
ATAR - 99.00+ plz... :)

Feel free to PM me for anything :D
Pages: [1] 2   Go Up