## Search found 76 matches

- Fri Dec 25, 2009 2:07 pm
- Forum: Number
- Topic: Digit-by-Digit Fibonacci-style Sequence
- Replies:
**4** - Views:
**3043**

### Re: Digit-by-Digit Fibonacci-style Sequence

The length of the cycle formed by Fibonacci mod 10 is 60. Let's say that as c(10)=60. While I was in college I proved, together with a friend of mine, the following facts about c: * If gcd(a,b)=1, then c(a*b) = lcm(c(a),c(b)) * If p is a prime and p=1(mod 5) or p=4(mod 5), then c(p) divides p-1 * If...

- Fri Aug 10, 2007 6:58 pm
- Forum: Number
- Topic: Grocery Store
- Replies:
**2** - Views:
**1184**

### Re: Grocery Store

About your food for thought: Do you know about the proof that all natural numbers have some special property? Well, assume it isn't so, and there are indeed natural numbers without any special properties. Let n be the smallest natural number without any special properties. Now, that's a very special...

- Tue Jul 17, 2007 6:40 pm
- Forum: Number
- Topic: "Summarizing" sequence
- Replies:
**11** - Views:
**2778**

### Re: "Summarizing" sequence

For more precise results in the line that rayfill was pursuing: http://en.wikipedia.org/wiki/Look-and-say_sequence Some hackish/fastish C++ code to compute the answer for 60 (not as fast as the reported assembly solution, but in the same order of magnitude): #include <iostream> char a[100000000]="1\...

- Tue May 01, 2007 2:38 am
- Forum: Number
- Topic: Patterns...
- Replies:
**7** - Views:
**2530**

I would use "cycle". But I don't know what you are looking for. If you want to find the cycle of one of these functions modulo a small number, it's trivial to make a little program to do so, and if I were to write out these cycles, I wouldn't know what sequences to put there. On this topic, there ar...

- Mon Apr 30, 2007 11:28 pm
- Forum: Number
- Topic: Patterns...
- Replies:
**7** - Views:
**2530**

- Mon Apr 30, 2007 10:48 pm
- Forum: Number
- Topic: Patterns...
- Replies:
**7** - Views:
**2530**

- Mon Apr 30, 2007 3:55 pm
- Forum: Number
- Topic: Patterns...
- Replies:
**7** - Views:
**2530**

### Re: Patterns...

What exactly do you mean when you say that "2x=" will create a cyclic group? (or any or the other lines, for that matter)

- Sat Mar 10, 2007 2:12 am
- Forum: Number
- Topic: Three squares make a sixth power
- Replies:
**8** - Views:
**3239**

- Wed Feb 21, 2007 3:55 pm
- Forum: Number
- Topic: Greatest Common Factors
- Replies:
**5** - Views:
**2332**

The usual axioms for probabilities on infinite sets are Kolmogorov's axioms: http://en.wikipedia.org/wiki/Probability_axioms The notion of "probability" over the naturals that you seem to be using is the following. Given a subset A of the natural numbers, one can count what fraction of the first n n...

- Wed Feb 21, 2007 2:38 pm
- Forum: Number
- Topic: Greatest Common Factors
- Replies:
**5** - Views:
**2332**

- Wed Feb 21, 2007 3:37 am
- Forum: Number
- Topic: Greatest Common Factors
- Replies:
**5** - Views:
**2332**

- Thu Feb 01, 2007 2:40 am
- Forum: Number
- Topic: Group Theory
- Replies:
**5** - Views:
**2078**

- Mon Jan 29, 2007 2:02 am
- Forum: Number Theory
- Topic: A Planet Problem
- Replies:
**7** - Views:
**2946**

... If no other planet looks at either A or B, you can remove them from the picture and use induction. There is one more possibility to consider (and eliminate) : ... Q [map] A [map] B [map] C ... No. Maybe I didn't express it clearly enough. A and B are the planets such that the distance between t...

- Sun Jan 28, 2007 7:35 am
- Forum: Number Theory
- Topic: A Planet Problem
- Replies:
**7** - Views:
**2946**

If you consider the two planets A and B that are closest to each other, A looks at B and B looks at A. If some other planet looks at either A or B, one planet is being watched more than once, so there must be an unwatched planet. If no other planet looks at either A or B, you can remove them from th...

- Tue Jan 23, 2007 3:37 am
- Forum: Number
- Topic: A prime property
- Replies:
**3** - Views:
**2072**

We need to find two quadratic residues modulo p that add up to -1. There are exactly (p-1)/2 quadratic residues modulo p, excluding 0. If -1 is a quadratic residue, we are done. If (p-1)/2 is a quadratic residue, we are also done. Now we consider the following (p-3)/2 sets: {1,p-2}, {2,p-3}, ..., {(...

- Fri Jan 19, 2007 7:01 pm
- Forum: Game Theory
- Topic: Grid Logic
- Replies:
**4** - Views:
**3855**

I would try something relatively simple, like breadth-first search.

- Fri Dec 29, 2006 6:18 pm
- Forum: Number Theory
- Topic: smallest multiple of 17 (urgent! )
- Replies:
**6** - Views:
**3544**

- Thu Nov 23, 2006 3:09 pm
- Forum: Number
- Topic: A Binary Number Puzzle
- Replies:
**3** - Views:
**2498**

I think I have a simple solution. Consider Any five q-digit binary numbers such that there is no place with a common digit for all the numbers. We are going to compare all pairs of numbers, and there are 10 pairs. That means that we are going to compare 10*q pairs of bits. How many matches will we g...

- Fri Nov 17, 2006 1:44 pm
- Forum: Number
- Topic: A Quadratic Divisor Puzzle
- Replies:
**3** - Views:
**2297**

- Wed Nov 15, 2006 2:51 am
- Forum: Number
- Topic: It just doesn't add up?!
- Replies:
**1** - Views:
**1554**

### Re: It just doesn't add up?!

No, it's (3*$9)-$2 which should equal $25, which is the price of the rooms,neonash7777 wrote:So we have (3*$9)+$2 which is suppose to equal $30