Team Test Fall Classic 2003
... 11) The teacher whispers positive integers A to Anna, B to Brett, and C to Chris. The students don’t know one another’s numbers but they do know that the sum of their numbers is 14. Anna says: “I know that Brett and Chris have different numbers.” Then Brett says: “I already knew that all three of ou ...
... 11) The teacher whispers positive integers A to Anna, B to Brett, and C to Chris. The students don’t know one another’s numbers but they do know that the sum of their numbers is 14. Anna says: “I know that Brett and Chris have different numbers.” Then Brett says: “I already knew that all three of ou ...
1 Lecture 1
... Definition 14. A positive integer p is called a prime if its only divisible by 1 and itself. A positive integer p, which is not a prime is called a composite number. Examples: 11 is a prime, 12 = 4 × 3 = 22 × 3 is composite. Theorem 14. The Fundamental Theorem of Arithmetics. Every positive integer ...
... Definition 14. A positive integer p is called a prime if its only divisible by 1 and itself. A positive integer p, which is not a prime is called a composite number. Examples: 11 is a prime, 12 = 4 × 3 = 22 × 3 is composite. Theorem 14. The Fundamental Theorem of Arithmetics. Every positive integer ...
What is a proof? - Computer Science
... The pigeonhole principle is a basic counting technique. It is illustrated in its simplest form as follows: We have n + 1 pigeons and n holes. We put all the pigeons in holes (in any way we want). The principle tells us that there must be at least one hole with at least two pigeons in it. Why is that ...
... The pigeonhole principle is a basic counting technique. It is illustrated in its simplest form as follows: We have n + 1 pigeons and n holes. We put all the pigeons in holes (in any way we want). The principle tells us that there must be at least one hole with at least two pigeons in it. Why is that ...
SUM OF TWO SQUARES Contents 1. Introduction 1 2. Preliminaries
... Furthermore, if ac ≡ bc (mod m) and c, m are relatively prime, then a ≡ b (mod m). We can now categorize the integers into classes based on their congruence modulo m, for some m > 1, by putting integers congruent to each other in the same class. Each integer is assigned one and only one such class, ...
... Furthermore, if ac ≡ bc (mod m) and c, m are relatively prime, then a ≡ b (mod m). We can now categorize the integers into classes based on their congruence modulo m, for some m > 1, by putting integers congruent to each other in the same class. Each integer is assigned one and only one such class, ...
