Mathematical Proofing: integer/number proofing Watch

Asian Philly
Badges: 4
Rep:
?
#1
Report Thread starter 1 year ago
#1
Hi I'm doing A level Edexel Maths and this is my first year and I'm having difficulty understanding what to do for these questions and how to prove them.
examples are:
1.Prove that every odd integer between 2 and 26 is either prime or the product of two primes
2.Prove that the sum of two consecutive square numbers between 1^2 to 8^2 is an odd number.
3. Prove that all cube numbers are either a multiple of 9 or 1 more or 1 less than a multiple of 9

Pleas give a full detail as to how you would start and show youve proved it, it would mean a lot
0
reply
RDKGames
Badges: 20
Rep:
?
#2
Report 1 year ago
#2
(Original post by Asian Philly)
Hi I'm doing A level Edexel Maths and this is my first year and I'm having difficulty understanding what to do for these questions and how to prove them.
examples are:
1.Prove that every odd integer between 2 and 26 is either prime or the product of two primes
2.Prove that the sum of two consecutive square numbers between 1^2 to 8^2 is an odd number.
3. Prove that all cube numbers are either a multiple of 9 or 1 more or 1 less than a multiple of 9

Pleas give a full detail as to how you would start and show youve proved it, it would mean a lot
Pretty straight-forward to just exhaust all these.

So for (1) you just need to show that the numbers 3,5,7,9,11,13,15,17,19,21,23 are all either prime, or a product of two primes. First step is to weed out all the primes out of this list, then deal with the rest as a product of two primes.

EDIT: Exhaust all of these, except (3) of course, forgot to mention. To prove (3), you need to consider what you get when you cube a general integer, and a general integer has either remainder 0, 1, or 2 when divided by 3.
0
reply
the bear
Badges: 20
Rep:
?
#3
Report 1 year ago
#3
i) consider the converse of this proposition.... if an odd number is neither prime nor the product of two primes then it must be the product of how many primes ?
0
reply
Notnek
  • Study Helper
Badges: 20
Rep:
?
#4
Report 1 year ago
#4
(Original post by Asian Philly)
Hi I'm doing A level Edexel Maths and this is my first year and I'm having difficulty understanding what to do for these questions and how to prove them.
examples are:
1.Prove that every odd integer between 2 and 26 is either prime or the product of two primes
2.Prove that the sum of two consecutive square numbers between 1^2 to 8^2 is an odd number.
3. Prove that all cube numbers are either a multiple of 9 or 1 more or 1 less than a multiple of 9

Pleas give a full detail as to how you would start and show youve proved it, it would mean a lot
For 3) I recommend using exhaustion by splitting it into 3 cases : numbers divisible by 3, numbers that leave a remainder of 1 when divided by 3 and numbers that leave a remainder of 2 when divided by 3.
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • Bournemouth University
    Clearing Open Day Undergraduate
    Wed, 31 Jul '19
  • Staffordshire University
    Postgraduate open event - Stoke-on-Trent campus Postgraduate
    Wed, 7 Aug '19
  • University of Derby
    Foundation Open Event Further education
    Wed, 7 Aug '19

Are you tempted to change your firm university choice on A-level results day?

Yes, I'll try and go to a uni higher up the league tables (147)
17.52%
Yes, there is a uni that I prefer and I'll fit in better (74)
8.82%
No I am happy with my course choice (497)
59.24%
I'm using Clearing when I have my exam results (121)
14.42%

Watched Threads

View All