simi4448
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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
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DFranklin
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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.
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simi4448
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(Original post by 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.
I've got the first part... but any ideas how to prove it using algebra?

Thanks in advance!
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mqb2766
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(Original post by simi4448)
I've got the first part... but any ideas how to prove it using algebra?

Thanks in advance!
What are you trying to prove - what have you got?
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mqb2766
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(Original post by CletusYeetus)
You'll probably need to use proof by induction. If you already know what this is, cool, you can skip the following paragraph.

....
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
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CletusYeetus
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(Original post by 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
Ah sorry, I assumed that it wouldn't affect anything as OP is a tutor, not a student in this situation.
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mqb2766
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(Original post by CletusYeetus)
Ah sorry, I assumed that it wouldn't affect anything as OP is a tutor, not a student in this situation.
If they were a tutor and couldn't make progress with the question, I'd be surprised.
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.
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DFranklin
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(Original post by CletusYeetus)
Ah sorry, I assumed that it wouldn't affect anything as you're a tutor, not a student in this situation.
So, since I'm unashamedly the forum's grumpy old man: did it not strike you as strange that the OP claims to be a tutor but has basically shown no evidence that they've put any work in on this themselves?

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...
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RDKGames
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(Original post by CletusYeetus)
Ah sorry, I assumed that it wouldn't affect anything as OP is a tutor, not a student in this situation.
Good effort but you can just square 3n, 3n+1, and 3n+2 to obtain the proof in just few lines to make life easy.
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Qxi.xli
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(Original post by CletusYeetus)
Ah sorry, I assumed that it wouldn't affect anything as OP is a tutor, not a student in this situation.
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
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Muttley79
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(Original post by 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
A tutor?!
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DFranklin
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(Original post by 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
Why would you want to do it by induction? It comes out in a few lines directly *once* you understand what the patterns are.
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DFranklin
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(Original post by Muttley79)
A tutor?!
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...
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Qxi.xli
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(Original post by 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.
Oh ok, it's just I don't know how else you'd prove it?
I might try it out later..
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DFranklin
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(Original post by Qxi.xli)
Oh ok, it's just I don't know how else you'd prove it?
I might try it out later..
Post #9 is a good starting point.
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Qxi.xli
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(Original post by DFranklin)
Post #9 is a good starting point.
Ah I got it, thanks.
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Muttley79
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(Original post by 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...
I've spent most of the week reporting people selling or wanting locked papers ... so disappointing
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davros
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(Original post by 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...
This "tutor" seems to need an awful lot of help on TSR this week
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DFranklin
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(Original post by Muttley79)
I've spent most of the week reporting people selling or wanting locked papers ... so disappointing
Thanks for at least trying - it's hard when I'm outside the loop of knowing what's locked etc. while seeing post after post that reeks of being an attempt to get information they shouldn't.
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Plücker
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(Original post by Muttley79)
A tutor?!
Actually, I could believe that.
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