26 Apr '08 15:24>
Is there a set of 2008 distinct positive integers, such that the sum of any 2007 of them is a perfect square?
Originally posted by David113The set must sum to X^2 + Y, where Y is the smallest member of the set.
Is there a set of 2008 distinct positive integers, such that the sum of any 2007 of them is a perfect square?
Originally posted by David113Solving this is a fools errand. We have to set it up so that
Is there a set of 2008 distinct positive integers, such that the sum of any 2007 of them is a perfect square?
Originally posted by UzumakiAiActually, there is a simple solution, without any hard work.
Solving this is a fools errand. We have to set it up so that
(>"#" denotes subtext)
N>"1" + N>"2"... N>"2007"= (S>"1" ) ^2
N>"1" + N>"3"... N>"2007"= (S>"2" ) ^2
N>"1" + N>"4"... N>"2007"= (S>"3" ) ^2
N>"1" + N>"5"... N>"2007"= (S>"4" ) ^2
etc.
There would be
2008!/2007!
equations, or 2008 equations, with
2008+2007=4015
variabl ...[text shortened]... I don't feel like finishing it! Ok?
Originally posted by David113Oh! Of course! It was yes/no question. Yes is the answer, it is always possible for a set of n numbers for there to be sums that are always perfect squares.
Actually, there is a simple solution, without any hard work.
Originally posted by DejectionI provided way to find the answer in the previous post, if you do that you will find the numbers. There is no way that there aren't any. The equations would work out.
Generally, asking whether something exists implies asking for a proof, not a straight answer.