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Sum of two squares

  1. Jun 9, 2015 #1
    Why bother writing a given integer as the sum of two squares? Does this have any practical application? Is there an introduction on a first year number theory course which would motivate students to study the conversion of a given integer to sums of two squares?
  2. jcsd
  3. Jun 9, 2015 #2
    There is a good deal of material. For instance the corollary to a theorem of Fermat :- "Any prime ##p## of the form ##4k+1## can be represented uniquely as the sum of 2 squares. Or (related) Lagrange's theorem:- "Any positive integer ##n## can be written as the sum of 4 squares, some of which may be 0".
    Then there are also many interesting properties of ##r_2(n)## where ##r## is the sum of squares function.
    I would recommend you research "representations of integers as sums of squares."
  4. Jun 9, 2015 #3
    It most likely does not. There are applications of number theory, but overall you should take the class mainly because you find it interesting, not because of possible applications.
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