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Matsh proof

Prove that the sum of three consecutive square numbers is one less than a multiple of 3

If u could use + (n+1)² + (n+2)² please
(edited 3 years ago)
Reply 1
Okay so I’ve checked it and I believe you can, first thing expand the brackets and sum everything up :smile: then tell me what you got and I’ll check
Reply 2
Original post by macy_m
Okay so I’ve checked it and I believe you can, first thing expand the brackets and sum everything up :smile: then tell me what you got and I’ll check

I got 3n²+6n+5 after expanding it all and adding them
Reply 3
Original post by Mystxgon
I got 3n² 6n 5 after expanding it all and adding them


So then you’d factorise the 3 our and be left with a 5 outside but that wouldn’t work so you’d have to have a -1 outside, do you know how you could word it then?
(edited 3 years ago)
So, what do you get if you add 1? Can you see why it's a multiple of 3?

Incidentally, you could also consider your 3 consecutive squares to be (n-1)^2, n^2, (n+1)^2, in which case symmetry is going to make your calculations slightly easier. No big deal here, but something to be aware of for harder problems.
(edited 3 years ago)
Reply 5
Original post by macy_m
So then you’d factorise the 3 our and be left with a +5 outside, do you know how you could word it then?

Thank u for the help i understand it now 3(n²+2n+2) -1 i believe?
Reply 6
Original post by Mystxgon
Thank u for the help i understand it now 3(n²+2n+2) -1 i believe?


Yes ! :biggrin:

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