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#1 2007-02-02 11:10:45

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Consecutive squares

Find 4 consecutive integers such that each one is divisible by a square.  No computer algorithms allowed, although a 4 function calculator may be used to increase the speed of calculations.  1 is not considered a square for this puzzle.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#2 2007-02-02 12:09:55

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Consecutive squares

What constitutes an algorithm? Does using Excel to help count? I'll just give a

instead of answering in case I've cheated.

Edit: Sorry, I got the hint wrong. I was thinking of the number 100 higher than the number I wanted. It is still divisible by a cube though.


Why did the vector cross the road?
It wanted to be normal.

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#3 2007-02-02 14:53:28

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Consecutive squares

Yes, excel is just one big algorithm, let alone how it lets you create your own algorithms.

Any program that runs on a computer must be some form of algorithm.

Also, your hint is incorrect.  That need not be the case, although in your solution it may be.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#4 2007-02-02 15:45:35

Toast
Real Member
Registered: 2006-10-08
Posts: 1,321

Re: Consecutive squares

Trial and error at the moment xD, god those numbers must be enormous.

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#5 2007-02-02 16:32:39

Zhylliolom
Real Member
Registered: 2005-09-05
Posts: 412

Re: Consecutive squares

Brute force might take you a while, write some ideas on what you can say about numbers with this property down on paper, and maybe some ideas will come to you.

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#6 2007-02-02 19:19:24

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Consecutive squares

I guess the real question is how did you come up with such solutions, Zhylliolom?


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#7 2007-03-01 00:44:14

George,Y
Member
Registered: 2006-03-12
Posts: 1,306

Re: Consecutive squares

Yes, I wonder what his idea was.

Last edited by George,Y (2007-03-01 00:44:31)


X'(y-Xβ)=0

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