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November 10th, 2011, 10:03 PM  #1 
Newbie Joined: Nov 2011 Posts: 1 Thanks: 0  Young Math Student
So my 9 yr old tonight pointed out the following. If X is any whole number and Y=X+1 Then (Y*Y)(X*X)=X+Y I have written out this equation for him but he came upon and expressed the pattern himself. Does anyone know anything about this equation. I would love to feed him some history. Thanks. Pround PAPA 
November 11th, 2011, 07:08 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Young Math Student
It's correct, and it even holds if X is a rational or real number instead of just a whole number. It would usually be expressed where is mathematical shorthand for "this thing times itself". It can be used to show a remarkable property: the sum of consecutive odd numbers (starting from 1) yields a square: and so forth. That's because to get from, say, to you need to add which is, as your 9yearold pointed out, the same as 3+4 = 7, expanding 1 + 3 + 5 to 1 + 3 + 5 + 7. Neat, huh? 

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