# Maths Proof Question Help

Watch
Announcements

I was given this question from the student I'm tutoring and need help to solve it algebraically...

prove that the square of any natural number is either a multiple of 3 or one more than a multiple of 3

Thanks in advance

prove that the square of any natural number is either a multiple of 3 or one more than a multiple of 3

Thanks in advance

Last edited by simi4448; 1 month ago

0

reply

Report

#2

Write out the squares of the first 10 or so natural numbers, see what their remainders are when divided by 3, look at the pattern, form a hypothesis, prove it.

0

reply

(Original post by

Write out the squares of the first 10 or so natural numbers, see what their remainders are when divided by 3, look at the pattern, form a hypothesis, prove it.

**DFranklin**)Write out the squares of the first 10 or so natural numbers, see what their remainders are when divided by 3, look at the pattern, form a hypothesis, prove it.

Thanks in advance!

0

reply

Report

#4

(Original post by

I've got the first part... but any ideas how to prove it using algebra?

Thanks in advance!

**simi4448**)I've got the first part... but any ideas how to prove it using algebra?

Thanks in advance!

0

reply

Report

#5

(Original post by

You'll probably need to use proof by induction. If you already know what this is, cool, you can skip the following paragraph.

**CletusYeetus**)You'll probably need to use proof by induction. If you already know what this is, cool, you can skip the following paragraph.

**...**.https://www.thestudentroom.co.uk/sho....php?t=4919248

Last edited by mqb2766; 1 month ago

0

reply

Report

#6

(Original post by

Admire the effort, but could you pls delete and read the forum sticky about not posting solutions, especially when the OP has not posted any attempt. Thanks.

https://www.thestudentroom.co.uk/sho....php?t=4919248

**mqb2766**)Admire the effort, but could you pls delete and read the forum sticky about not posting solutions, especially when the OP has not posted any attempt. Thanks.

https://www.thestudentroom.co.uk/sho....php?t=4919248

Last edited by CletusYeetus; 1 month ago

1

reply

Report

#7

(Original post by

Ah sorry, I assumed that it wouldn't affect anything as OP is a tutor, not a student in this situation.

**CletusYeetus**)Ah sorry, I assumed that it wouldn't affect anything as OP is a tutor, not a student in this situation.

Thanks for deleting. For info, induction is overkill, you had the right breakdown, but some simple algebra would get there more directly. Dont want to say more for obvious reasons.

Last edited by mqb2766; 1 month ago

0

reply

Report

#8

(Original post by

Ah sorry, I assumed that it wouldn't affect anything as you're a tutor, not a student in this situation.

**CletusYeetus**)Ah sorry, I assumed that it wouldn't affect anything as you're a tutor, not a student in this situation.

There's a reason I wrote my original response in a fairly terse "I'm going to give you lots of opportunities to do some work yourself" kind of a fashion...

0

reply

Report

#9

**CletusYeetus**)

Ah sorry, I assumed that it wouldn't affect anything as OP is a tutor, not a student in this situation.

1

reply

Report

#10

**CletusYeetus**)

Ah sorry, I assumed that it wouldn't affect anything as OP is a tutor, not a student in this situation.

0

reply

Report

#11

(Original post by

I was given this question from the student I'm tutoring and need help to solve it algebraically...

prove that the square of any natural number is either a multiple of 3 or one more than a multiple of 3

Thanks in advance

**simi4448**)I was given this question from the student I'm tutoring and need help to solve it algebraically...

prove that the square of any natural number is either a multiple of 3 or one more than a multiple of 3

Thanks in advance

0

reply

Report

#12

(Original post by

Hey I'm not OP but could you send me what you wrote about using proof by induction, maybe by PM? I'm just curious lol. I'm sure I could do it if I wanted to but I'm feeling a little lazy and it won't be a waste of your writing that way either

**Qxi.xli**)Hey I'm not OP but could you send me what you wrote about using proof by induction, maybe by PM? I'm just curious lol. I'm sure I could do it if I wanted to but I'm feeling a little lazy and it won't be a waste of your writing that way either

0

reply

Report

#13

(Original post by

A tutor?!

**Muttley79**)A tutor?!

You know how it goes... {Sigh}

Sorry to be so cynical, but most of the posts over the last week have not been terribly edifying...

1

reply

Report

#14

(Original post by

Why would you want to do it by induction? It comes out in a few lines directly *once* you understand what the patterns are.

**DFranklin**)Why would you want to do it by induction? It comes out in a few lines directly *once* you understand what the patterns are.

I might try it out later..

0

reply

Report

#15

(Original post by

Oh ok, it's just I don't know how else you'd prove it?

I might try it out later..

**Qxi.xli**)Oh ok, it's just I don't know how else you'd prove it?

I might try it out later..

0

reply

Report

#16

(Original post by

Post #9 is a good starting point.

**DFranklin**)Post #9 is a good starting point.

1

reply

Report

#17

(Original post by

A "tutor"; probably for a student who "knows the solution already but just wants someone else to prove it so they can check"...

You know how it goes... {Sigh}

Sorry to be so cynical, but most of the posts over the last week have not been terribly edifying...

**DFranklin**)A "tutor"; probably for a student who "knows the solution already but just wants someone else to prove it so they can check"...

You know how it goes... {Sigh}

Sorry to be so cynical, but most of the posts over the last week have not been terribly edifying...

0

reply

Report

#18

**DFranklin**)

A "tutor"; probably for a student who "knows the solution already but just wants someone else to prove it so they can check"...

You know how it goes... {Sigh}

Sorry to be so cynical, but most of the posts over the last week have not been terribly edifying...

0

reply

Report

#19

(Original post by

I've spent most of the week reporting people selling or wanting locked papers ... so disappointing

**Muttley79**)I've spent most of the week reporting people selling or wanting locked papers ... so disappointing

0

reply

X

### Quick Reply

Back

to top

to top