anyone interested in this?
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From: [log in to unmask]
Date sent: Wed, 03 Mar 1999 13:06:43 -0500
Subject: PYTHAGOREAN TRIPLES
I NOTE THAT ALL PYTHAGOREAN TRIPLES CAN BE COMMUTATIVELY EXPRESSED,AS THE
SUM OF COSECUTIVE, ODD,INTEGERS,TWO WITHIN THE CONFINES OF THE THIRD,E.G.
5SQUARED=3SQUARED+4SQUARED=4SQUARED+3SQUARED=[1+3+5+7+9]=[1+3+5]+[7+9]=
[1+3+5+7]+[9],BY VIRTUE OF THE COMMUTATIVE PROPERTY OF ADDITION,AND AS
CORRESPONDINGLY BRACKETED.
SIMILARLY,13SQUARED=5SQUARED+12SQUARED=12SQUARED+5SQUARED=
[1+3+5+7+9+11+13+15+17+19+21+23+25]=[1+3+5+7+9]+[11+13+15+17+19+21+23+25]=
[1+3+5+7+9+11+13+15+17+19+21+23]+[25] AS CORRESPONDINGLY BRACKETED,AND SO
ON FOR ALL
PYTHAGOREAN TRIPLES,AND THERE IS AN INFINITE NUMBER OF THEM.
SURELY,THERE MUST BE A FORMAL,ALGEBRAIC,PROOF OF THIS
SIMPLE,COMMUTATIVE,PROPERTY THAT IS UNIQUE TO SQUARES,AND
NEVER TO CUBES,OR ANY OTHER HIGHER POWER?
I HAVE SEARCHED EVERYWHERE WITHOUT SUCCESS.PERHAPS,YOUR MATHEMATICS
DEPARTMENT MAY
CONTRIBUTE .I'D APPRECIATE YOUR HELP.THANK YOU.
KIND REGARDS,
SINCERELY,
T.P. WOODS.
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