Letter to the Editor
... I'm afraid there was an error in the February issue of The Fibonacci Quarterly. Mr. Shallit's proof that phi is irrational is correct up to the point where he claims that 1/0 can't be an integer. He has no basis for making that claim, as 0 was defined as a rational number, not an integer. The proof ...
... I'm afraid there was an error in the February issue of The Fibonacci Quarterly. Mr. Shallit's proof that phi is irrational is correct up to the point where he claims that 1/0 can't be an integer. He has no basis for making that claim, as 0 was defined as a rational number, not an integer. The proof ...
MATHEMATICAL INDUCTION
... one needs to conjecture the underlying rule, and then verify whether it is, indeed, correct. In other words, we have to do some guessing. The following examples elucidate this point. Example 3.1. For what values on n is 2n + 1 a multiple of 3? Solution. By checking small values of the integer n one ...
... one needs to conjecture the underlying rule, and then verify whether it is, indeed, correct. In other words, we have to do some guessing. The following examples elucidate this point. Example 3.1. For what values on n is 2n + 1 a multiple of 3? Solution. By checking small values of the integer n one ...
![B2[∞]-sequences of square numbers](http://s1.studyres.com/store/data/014554791_1-cdd0f3de1fbdb07bf0c0f87a9c563b95-300x300.png)
![[Part 1]](http://s1.studyres.com/store/data/008795787_1-e53528a6e716c9914682cf7824ec41a5-300x300.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.