Gaussian rationals ℚ(i)

Target entity: Gaussian rationals ℚ(i)
Context triple: [Gaussian integers, fieldOfFractions, Gaussian rationals ℚ(i)]

• A. Gaussian integers
  Gaussian integers are complex numbers whose real and imaginary parts are both integers, forming a lattice in the complex plane with important applications in number theory and algebra.
• B. Gauss’s lemma in number theory
  Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
• C. Gauss’s constant
  Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
• D. Fermat's theorem on sums of two squares
  Fermat's theorem on sums of two squares is a result in number theory stating exactly which prime numbers (and, more generally, which integers) can be expressed as the sum of two perfect squares.
• E. Disquisitiones Arithmeticae
  Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Gaussian rationals ℚ(i)
Target entity description: Gaussian rationals ℚ(i) are the field of complex numbers whose real and imaginary parts are rational, formed by adjoining the imaginary unit i to the rational numbers.

• A. Gaussian integers
  Gaussian integers are complex numbers whose real and imaginary parts are both integers, forming a lattice in the complex plane with important applications in number theory and algebra.
• B. Gauss’s lemma in number theory
  Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
• C. Gauss’s constant
  Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
• D. Fermat's theorem on sums of two squares
  Fermat's theorem on sums of two squares is a result in number theory stating exactly which prime numbers (and, more generally, which integers) can be expressed as the sum of two perfect squares.
• E. Disquisitiones Arithmeticae
  Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
• F. None of above. chosen