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 March 12th, 2013, 11:57 AM #1 Member   Joined: Jan 2013 Posts: 96 Thanks: 0 Integers Prove that there are infinitely many integers numbers: $m,a,b,c \in \mathbb{Z}$ such that $m^2=a^2+b^2+c^2$!
 March 12th, 2013, 01:50 PM #2 Member   Joined: Mar 2013 Posts: 90 Thanks: 0 Re: Integers Set $a=b=0,\,c=m$.
 March 12th, 2013, 02:45 PM #3 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Integers Prove the stronger statement: there are infinitely many positive integers m such that m^2 = a^2 + b^2 + c^2 for a, b, and c positive integers. (For more of a challenge, show that such m are of density 1 in the positive integers.)
 March 13th, 2013, 12:58 PM #4 Member   Joined: Jan 2013 Posts: 96 Thanks: 0 Re: Integers I forgot to write that a,b,c are different by 0 !
 March 17th, 2013, 01:50 AM #5 Member   Joined: Feb 2011 Posts: 68 Thanks: 0 Re: Integers find zs such that a^2+b^2=z^2 and z^2+c^2=m^2. for example (3*3)^2+(4*3)^2=(5*3)^2 and (3*5)^2+(4*5)^2=(5*5)^2.

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