#1
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A challenging Number Theory problem
Show that if A and B can be written as the sum of the squares of 4 integers , then so can their product A*B .
I found this question to be very difficult . |
#2
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Re: A challenging Number Theory problem
First of all, Lagrange proved that every non-negative
integer can be written as a sum of four squares (and since the product of two non-negative integers is a non-negative integer, it's clear). What you are asking for is probably Euler's four-square identity; here's a link to Wikipedia: http://en.wikipedia.org/wiki/Euler%2...quare_identity |
#3
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Re: A challenging Number Theory problem
I didn't know that this was attributed to Euler , but thx for the link .
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#4
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Re: A challenging Number Theory problem
Fermat conjectured that every number would be the sum of n n-agonal numbers.
Gauss proved for triangular (1796), Lagrange for squares (1770) and Cauchy proved the whole thing in 1813. Awesome theorem. |
#5
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Re: A challenging Number Theory problem
I've read about the result (first time was in Apostol's
book on analytic number theory), but haven't looked at the proof. A very nice theorem indeed! |
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