About: Thue's lemma

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In additive number theory, Fermat's theorem on sums of two squares states that an odd prime p can be expressed as: with x and y integers, if and only if The prime numbers for which this is true are called Pythagorean primes.For example, the primes 5, 13, 17, 29, 37 and 41 are all congruent to 1 modulo 4, and they can be expressed as sums of two squares in the following ways:

Attributes	Values
rdfs:label	Fermat's theorem on sums of two squares (en)
rdfs:comment	In additive number theory, Fermat's theorem on sums of two squares states that an odd prime p can be expressed as: with x and y integers, if and only if The prime numbers for which this is true are called Pythagorean primes.For example, the primes 5, 13, 17, 29, 37 and 41 are all congruent to 1 modulo 4, and they can be expressed as sums of two squares in the following ways: (en)
sameAs	Thue's lemma Thue's lemma
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Subject	Additive number theory Squares in number theory Theorems in number theory
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Fermat's_theorem_on_sums_of_two_squares?oldid=1064865677&ns=0
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Link from a Wikipage to another Wikipage	Marin Mersenne Proof by infinite descent Root of unity Sum of two squares theorem Unique factorization domain Unit (ring theory) Unit cell A K Peters Absolute value Additive number theory Albert Girard Algebraic integer Algorithm Binary quadratic form Blaise Pascal Radix Thue's lemma Vorlesungen über Zahlentheorie Brahmagupta–Fibonacci identity Carl Friedrich Gauss Additive number theory Squares in number theory Theorems in number theory Joseph-Louis Lagrange Joseph Liouville Discriminant Disquisitiones Arithmeticae Don Zagier Legendre's three-square theorem Leonard Eugene Dickson Leonhard Euler Peter Gustav Lejeune Dirichlet Pierre de Fermat Pythagorean prime Quadratic field Quadratic form Quadratic reciprocity Quadratic residue Without loss of generality Christian Goldbach Prime element Prime ideal Prime number Principal ideal domain Time complexity Complex number Computational complexity History of the Theory of Numbers Minkowski's theorem Order (group theory) Parity (mathematics) Partition (number theory) Finite difference Fixed-point theorems Frobenius endomorphism Fundamental theorem of arithmetic Gaussian integer Ideal (ring theory) Ideal norm If and only if Exponential function Fermat's little theorem Harold Edwards (mathematician) Integral domain Involution (mathematics) John Stillwell Lagrange's four-square theorem Modular arithmetic Vector space Euclidean algorithm Euclidean division Euclidean domain Euler's criterion Euler characteristic

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