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# Proof question check watch

1. My first thread ok basically just a quick check to see how many marks out of ten id get for this proof. Any more elegant solutions welcome
The question was whether the product of 2 consecutive numbers could ever equal product of 4 consecutive numbers
my proof product for consecutive =a(a+1)(a+2)(a+3)=a^4+6n^3+11n^2 +6n
Which equals (n+3n+1)^2-1 this shows that 4 consecutive numbers always make a number 1 less than a square number
Now two consecutive numbers multiplied make b^2+b. The difference between square of b and the number a bove is b+(b+1) now the only way b^2+b can be a square is if the number above b=1 so b=0 but the proof is for positive numbers (forgot to mention that) so no two consecutive numbers multiplied can never be equal to the product of four(for positive integers)
How many marks would this get thnx
2. "a(a+1)(a+2)(a+3)=a^4+6n^3+1 1n^2 +6n"

Where did the n come from? And where did the a go later? Also I don't really follow the last bit.
3. (Original post by Anony1234)
The difference between square of b and the number a bove is b+(b+1) now the only way b^2+b can be a square is if the number above b=1 so b=0 but the proof is for positive numbers (forgot to mention that) so no two consecutive numbers multiplied can never be equal to the product of four(for positive integers)
How many marks would this get thnx
Couldn't really follow the part quoted.

A minor change:

We require

(n+3n+1)^2-1=b^2+b

Adding 1 to each side, we require

b^2+b+1 to be a perfect square.

But b^2 < b^2+b+1 < (b+1)^2

for b>0 and hence cannot be a perfect square.
4. (Original post by ghostwalker)
Couldn't really follow the part quoted.

A minor change:

We require

(n+3n+1)^2-1=b^2+b

Adding 1 to each side, we require

b^2+b+1 to be a perfect square.

But b^2 < b^2+b+1 < (b+1)^2

for b>0 and hence cannot be a perfect square.
Oh yeah i basically did that on paper just typed it out in a rush. What iw as trying to say was that the difference between a square b and the next square is b+b+1 eg from 3 squared you add 3 +4= 7 to it to get 4 squared you get like you said b square + b + 1 to make a square. It has no chance of being b square but it you repace the (b+1) bit for the next square with 1 it could work. However as b is more than 0 its not possible. How many would this get out of ten thnx for the help
5. (Original post by james22)
"a(a+1)(a+2)(a+3)=a^4+6n^3+1 1n^2 +6n"

Where did the n come from? And where did the a go later? Also I don't really follow the last bit.
Just me typing in arush its actually all a not nso replace n with a
6. (Original post by Anony1234)
Oh yeah i basically did that on paper just typed it out in a rush. What iw as trying to say was that the difference between a square b and the next square is b+b+1 eg from 3 squared you add 3 +4= 7 to it to get 4 squared you get like you said b square + b + 1 to make a square. It has no chance of being b square but it you repace the (b+1) bit for the next square with 1 it could work. However as b is more than 0 its not possible. How many would this get out of ten thnx for the help
My guess 9 /10. With +/- 1 depending on how easy the examiner can understand what you're saying and how generous they are. Improving your layout and presentation (i.e. don't rush) would make it easier for the examiner to follow. If you'd done, on paper, what I posted, I'd expect 10; IMHO.

The a to n would probably lose you a mark too, but depends on the examiner's generosity.
7. (Original post by ghostwalker)
My guess 9 /10. With +/- 1 depending on how easy the examiner can understand what you're saying and how generous they are. Improving your layout and presentation (i.e. don't rush) would make it easier for the examiner to follow. If you'd done, on paper, what I posted, I'd expect 10; IMHO.

The a to n would probably lose you a mark too, but depends on the examiner's generosity.
Oh thk you very and can i pls ask you this can you go here and help me with the answer i no im only in yr 10 but its been bugging me for ages
http://www.thestudentroom.co.uk/show...highlight=Ukmt

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