Math Is Fun Forum

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.

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"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..."

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.

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

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.

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"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..."

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.

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.

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?

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"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..."

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Consecutive squares

Yes, I wonder what his idea was.

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

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