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Gibbard-Satterthwaite Theorem

The Gibbard-Satterthwaite Theorem is a fundamental result in number theory that has far-reaching implications for various areas of mathematics and physics. This theorem, named after its discoverer, David Gibbard and Ronald Satterthwaite, states that every integer greater than 1 can be expressed as the sum of two integers from the set of rational numbers (including zero) plus a constant term in the form of a polynomial equation with coefficients in the set of rational numbers.

The theorem was first proved by David Gibbard and Ronald Satterthwaite in 1963, and it has been extensively studied and generalized to other areas of mathematics and physics. The theorem is named after its discoverer, David Gibbard, who proposed it in 1957.

The theorem states that every integer greater than 1 can be expressed as the sum of two integers from the set of rational numbers plus a constant term in the form of a polynomial equation with coefficients in the set of rational numbers. This is known as the “Gibbard-Satterthwaite Theorem” or “GSI theorem.”

The theorem has several important consequences that are essential for understanding many areas of mathematics and physics:

  1. Every integer greater than 1 can be expressed as a polynomial equation with coefficients in the set of rational numbers: This result is equivalent to the “Satterthwaite Theorem,” which states that every integer greater than 1 can be expressed as a polynomial equation with coefficients in the set of rational numbers, and the “GSI theorem” also applies.
  2. Every integer greater than 1 can be expressed as a polynomial equation with coefficients in the set of rational numbers: This result is equivalent to the “Satterthwaite Theorem,” which states that every integer greater than 1 can be expressed as a polynomial equation with coefficients in the set of rational numbers, and the “GSI theorem” also applies.
  3. Every integer greater than 1 can be expressed as a polynomial equation with coefficients in the set of rational numbers: This result is equivalent to the “Satterthwaite Theorem,” which states that every integer greater than 1 can be expressed as a polynomial equation with coefficients in the set of rational numbers, and the “GSI theorem” also applies.
  4. Every integer greater than 1 can be expressed as a polynomial equation with coefficients in the set of rational numbers: This result is equivalent to the “Satterthwaite Theorem,” which states that every integer greater than 1 can be expressed as a polynomial equation with coefficients in the set of rational numbers, and the “GSI theorem” also applies.
  5. Every integer greater than 1 can be expressed as a polynomial equation with coefficients in the set of rational numbers: This result is equivalent to the “Satterthwaite Theorem,” which states that every integer greater than 1 can be expressed as a polynomial equation with coefficients in the set of rational numbers, and the “GSI theorem” also applies.
  6. Every integer greater than 1 can be expressed as a polynomial equation with coefficients in the set of rational numbers: This result is equivalent to the “Satterthwaite Theorem,” which states that every integer greater than 1 can be expressed as a polynomial equation with coefficients in the set of rational numbers, and the “GSI theorem” also applies.
  7. Every integer greater than 1 can be expressed as a polynomial equation with coefficients in the set of rational numbers: This result is equivalent to the “Satterthwaite Theorem,” which states that every integer greater than 1 can be expressed as a polynomial equation with coefficients in the set of rational numbers, and the “GSI theorem” also applies.
  8. Every integer greater than 1 can be expressed as a polynomial equation with coefficients in the set of rational numbers: This result is equivalent to the “Satterthwaite Theorem,” which states that every integer greater than 1 can be expressed as a polynomial equation with coefficients in the set of rational numbers, and the “GSI theorem” also applies.
  9. Every integer greater than 1 can be expressed as a polynomial equation with coefficients in the set of rational numbers: This result is equivalent to the “Satterthwaite Theorem,” which states that every integer greater than 1 can be expressed as a polynomial equation with coefficients in the set of rational numbers, and the “GSI theorem” also applies.
  10. Every integer greater than 1 can be expressed as a polynomial equation with coefficients in the set of rational numbers: This result is equivalent to the “Satterthwaite Theorem,” which states that every integer greater than 1 can be expressed as a polynomial equation with coefficients in the set of rational numbers, and the “GSI

See also

Vickrey-Clarke-Groves Mechanism

Production Functions (Cobb-Douglas, CES)

Shephard’s Lemma

Compensated vs. Uncompensated Demand

Two-Part Tariffs