Fermat Proved That Every Odd Prime Number Can Be Expressed

question 14

Essay

Fermat proved that every odd prime number can be expressed as the difference of two
squares in one and only one way. Express each of the first 6 odd prime numbers as the
difference of two squares.

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Definitions:

Antitrust Laws

Laws designed to promote competition and prevent monopolies, thereby protecting consumers from unfair business practices and ensuring a variety of goods and services in the market.

Sherman Act

A foundational antitrust law in the United States that outlaws monopolistic practices and promotes competitive markets.

Clayton Act

A U.S. legislation enacted in 1914 aimed at promoting competition among businesses by prohibiting certain practices that would lead to antitrust issues.

Herfindahl Index

A measure of the concentration and competitiveness of an industry; calculated as the sum of the squared percentage market shares of the individual firms in the industry.