Solutions - Stony Brook Math Department
... Alternatively, we could have used the sequences de nition. Let ...
... Alternatively, we could have used the sequences de nition. Let ...
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Multiplying and Dividing Integers - Black Problems
... The smallest common integer is 59. I tried to see a pattern with dividing by 2, 3, 4, and 5 and with their respective smallest integers: 5, 11, and 59. I came up with the following solution: The least common multiple of 2 and 3 is 6, the least common multiple of 2, 3 and 4 is 12, and the least commo ...
... The smallest common integer is 59. I tried to see a pattern with dividing by 2, 3, 4, and 5 and with their respective smallest integers: 5, 11, and 59. I came up with the following solution: The least common multiple of 2 and 3 is 6, the least common multiple of 2, 3 and 4 is 12, and the least commo ...
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... created: h2013-03-21i by: hbbukhi version: h32724i Privacy setting: h1i hDefinitioni h05A10i † This text is available under the Creative Commons Attribution/Share-Alike License 3.0. You can reuse this document or portions thereof only if you do so under terms that are compatible with the CC-BY-SA li ...
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.