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# 8: Topics in Number Theory

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• 8.1: The Greatest Common Divisor
One of the most important concepts in elementary number theory is that of the greatest common divisor of two integers. Let a and b be integers, not both 0. A common divisor of a and b is any nonzero integer that divides both a and b . The largest natural number that divides both a and b is called the greatest common divisor of a and b .
• 8.2: Prime Numbers and Prime Factorizations
• 8.3: Linear Diophantine Equations
Very little is known about Diophantus’ life except that he probably was the first to use letters for unknown quantities in arithmetic problems. His famous work, Arithmetica, consists of approximately 130 problems and solutions; most of solutions of equations in various numbers of variables. While Diophantus did not restrict his solutions to the integers and recognized rational number solutions as well, today, however, the solutions for a so-called Diophantine equation must be integers.
• 8.S: Topics in Number Theory (Summary)

Thumbnail: Golden spiral. Assuming a square has the side length of 1, the next smaller square is 1/φ wide. Then a width of 1/φ², 1/φ³ and so on. Image used with permission (Public Domain; Jahobr).