history-page11 - Definitions • Background “Natural...

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Unformatted text preview: Definitions • Background: “Natural numbers” means “numbers”. • m | n , m divides n , m is a factor of n , m is a divisor of n , n is a multiple of m : There is a number q such that qm = n . • m is prime if it has exactly two divisors. (Thus, 1 is not prime.) • m is composite if it has more than 2 divisors. (Thus, 1 is not composite.) • m and n are relatively prime if 1 is their greatest common divisor. Figurate Numbers • The Pythagoreans were also impressed by numbers that naturally correspond to simple geometric figures. • Triangular numbers • Square numbers • Etc. (Cooke is wrong about the regularity of these?) Perfect Numbers • Ascribed to Pythagoras (6th century BC). • m is perfect if the sum of its divisors other than itself equals itself. • m and n are amicable if the sum of m ’s divisors other than m equals n , and the sum of n ’s divisors other than n equals m ....
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This note was uploaded on 12/29/2011 for the course MATH 378 taught by Professor Wen during the Fall '10 term at SUNY Stony Brook.

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