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The Collatz conjecture is: This process will eventually reach the number 1, regardless of which positive integer is chosen initially. That is, for each , there is some with . If the conjecture is false, it can only be because there is some starting number which gives rise to a sequence that does not contain 1.
KooBits (stylised as KooBits with capitalised K and B) designs and builds digital products for children and educators. KooBits was founded in 2016 by current CEO Stanley, with Professor Sam Ge Shuzhi and Dr Chen Xiangdong. [1] The trio saw an opportunity in the rapid growth of the ebook industry and decided to focus on creating software for ...
One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes.”. You check this in your ...
These numbers also give the solution to certain enumerative problems, the most common of which is that of counting the number of ways of writing a given number n as an ordered sum of 1s and 2s (called compositions); there are F n+1 ways to do this (equivalently, it's also the number of domino tilings of the rectangle).
Sum and Product Puzzle. The Sum and Product Puzzle, also known as the Impossible Puzzle because it seems to lack sufficient information for a solution, is a logic puzzle. It was first published in 1969 by Hans Freudenthal, [1] [2] and the name Impossible Puzzle was coined by Martin Gardner. [3] The puzzle is solvable, though not easily.
There seems to be a discrepancy, as there cannot be two answers ($29 and $30) to the math problem. On the one hand it is true that the $25 in the register, the $3 returned to the guests, and the $2 kept by the bellhop add up to $30, but on the other hand, the $27 paid by the guests and the $2 kept by the bellhop add up to only $29. Solution
The Erdős distinct distances problem. The correct exponent was proved in 2010 by Larry Guth and Nets Katz, but the correct power of log n is still undetermined. The Erdős–Rankin conjecture on prime gaps, proved by Ford, Green, Konyagin, and Tao in 2014. The Erdős discrepancy problem on partial sums of ±1-sequences.
History In about 300 BC Euclid showed that if 2 p − 1 is prime then 2 p −1 (2 p − 1) is perfect. The first four perfect numbers were the only ones known to early Greek mathematics, and the mathematician Nicomachus noted 8128 as early as around AD 100. In modern language, Nicomachus states without proof that every perfect number is of the form 2 n − 1 (2 n − 1) {\displaystyle 2^{n-1 ...
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