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March 12th, 2013, 11:57 AM   #1
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Integers

Prove that there are infinitely many integers numbers: such that !
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March 12th, 2013, 01:50 PM   #2
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Re: Integers

Set .
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March 12th, 2013, 02:45 PM   #3
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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.)
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March 13th, 2013, 12:58 PM   #4
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Re: Integers

I forgot to write that a,b,c are different by 0 !
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March 17th, 2013, 01:50 AM   #5
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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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