2CH12L2 - VincentPienaar
... Divide by 2. Subtract 3. Function Rule B: Square the input. Subtract 6. Divide by 2. If the input value for each rule is 222, what is the difference of the two output values? Why? 0; they are equivalent rules. Course 2 ...
... Divide by 2. Subtract 3. Function Rule B: Square the input. Subtract 6. Divide by 2. If the input value for each rule is 222, what is the difference of the two output values? Why? 0; they are equivalent rules. Course 2 ...
SOLUTIONS TO HOMEWORK 3 1(a).
... a primitive root implies the order is strictly less than 36. The order must be a divisor of 36 (sketch of proof: if b is the order and b does not divide 36, then by division with remainder we get some 0 < r < b such that ar = a36−qb = 1 ∗ 1, which contradicts our assumption that the order was b). By ...
... a primitive root implies the order is strictly less than 36. The order must be a divisor of 36 (sketch of proof: if b is the order and b does not divide 36, then by division with remainder we get some 0 < r < b such that ar = a36−qb = 1 ∗ 1, which contradicts our assumption that the order was b). By ...
![arXiv:math/0608068v1 [math.NT] 2 Aug 2006](http://s1.studyres.com/store/data/016444901_1-15a2bfb469428d063b2c2745e8d56343-300x300.png)
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.