A Conjecture of Erd˝os the Ramsey Number r(W
... no 4-chromatic graph. Thus, r(G) > 18 = r(K4 ). The only 4-chromatic graph with 4, 5, or 6 vertices that does not contain a K4 is the wheel W6 = K1 + C5 with 6 vertices. Thus, the Erdős conjecture in the case k = 4 is equivalent to r(W6 ) ≥ 18 (strict inequality in the strong form of the conjectur ...
... no 4-chromatic graph. Thus, r(G) > 18 = r(K4 ). The only 4-chromatic graph with 4, 5, or 6 vertices that does not contain a K4 is the wheel W6 = K1 + C5 with 6 vertices. Thus, the Erdős conjecture in the case k = 4 is equivalent to r(W6 ) ≥ 18 (strict inequality in the strong form of the conjectur ...
22C:19 Discrete Math
... Encryption algorithms heavily depend on modular arithmetic, and our ability to deal with large integers. We need appropriate techniques to deal with such algorithms. ...
... Encryption algorithms heavily depend on modular arithmetic, and our ability to deal with large integers. We need appropriate techniques to deal with such algorithms. ...
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... Composite Numbers – are divisible by more than two numbers. Tell whether each number is prime or composite. (hint: use the divisibility rules!) ...
... Composite Numbers – are divisible by more than two numbers. Tell whether each number is prime or composite. (hint: use the divisibility rules!) ...
Chapter #2 Lecture Notes
... When you compare the multiples of two (or more) numbers, if they have any in common, they are called a common multiple of those numbers. The Least Common Multiple (referred to as the LCM) is the smallest common multiple of two (or more) numbers. Looking at the multiples of 5 and 7 above, what ...
... When you compare the multiples of two (or more) numbers, if they have any in common, they are called a common multiple of those numbers. The Least Common Multiple (referred to as the LCM) is the smallest common multiple of two (or more) numbers. Looking at the multiples of 5 and 7 above, what ...
Collatz conjecture
The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture (after Stanisław Ulam), Kakutani's problem (after Shizuo Kakutani), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem; the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), or as wondrous numbers.Take any natural number n. If n is even, divide it by 2 to get n / 2. If n is odd, multiply it by 3 and add 1 to obtain 3n + 1. Repeat the process (which has been called ""Half Or Triple Plus One"", or HOTPO) indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1. The property has also been called oneness.Paul Erdős said about the Collatz conjecture: ""Mathematics may not be ready for such problems."" He also offered $500 for its solution.