Die Suche ergab 102 Treffer
- 21.03.2011 20:30
- Forum: Fehler, Wünsche / Bugs, Wishes
- Thema: [sub-project] Perfect cuboid
- Antworten: 260
- Zugriffe: 312105
Re: [sub-project] Perfect cuboid
From Theorems 1 and 2 implies that the prime number p>2 can not be represented as a sum of two squares if it has a view of 4k+3, and can be presented, if p= 4k+1 Criterion Girard . Natural number can be represented as a sum of squares of two integers if and only if in its decomposition into simple f...
- 21.03.2011 20:25
- Forum: Fehler, Wünsche / Bugs, Wishes
- Thema: [sub-project] Perfect cuboid
- Antworten: 260
- Zugriffe: 312105
Re: [sub-project] Perfect cuboid
Theorem 2. Any prime number p form 4k+1 can be represented as a sum of squares of two integers. The proof consists of two lemmas: Lemma 2. For any prime p form 4k +1 there exists an integer m, that m²+1 is multiple p Lemma 3. Any prime divisors p of number m²+1, where m - integer, can be represente...
- 21.03.2011 20:13
- Forum: Fehler, Wünsche / Bugs, Wishes
- Thema: [sub-project] Perfect cuboid
- Antworten: 260
- Zugriffe: 312105
Re: [sub-project] Perfect cuboid
Theorem 1. Any odd number that can be represented as the sum of two squares has the form 4k+1 Proof: Between two integers whose sum of squares is odd, one number is necessarily even and the other is odd. The square of even number is divisible by 4 completely and the square of odd number of the divi...
- 21.03.2011 20:08
- Forum: Fehler, Wünsche / Bugs, Wishes
- Thema: [sub-project] Perfect cuboid
- Antworten: 260
- Zugriffe: 312105
Re: [sub-project] Perfect cuboid
If perfect cuboid exists, space diagonal of minimal cuboid (cuboid of minimal size) is the product of primes 4k+1. The proof of this lemma below.
- 21.03.2011 19:59
- Forum: Fehler, Wünsche / Bugs, Wishes
- Thema: [sub-project] Perfect cuboid
- Antworten: 260
- Zugriffe: 312105
Re: [sub-project] Perfect cuboid
Hello, guys! I opened this topic to share with you my original idea how we would continue a searching of perfect cuboid far away from 10^11 integers space. Our goal is to check all space diagonals up to 2^63 (9'223'372'036'854'775'808) If you are interested to participate, join us! We need mathemati...
- 21.03.2011 19:48
- Forum: Fehler, Wünsche / Bugs, Wishes
- Thema: [sub-project] Perfect cuboid
- Antworten: 260
- Zugriffe: 312105
[sub-project] Perfect cuboid
Perfect Cuboid http://mathworld.wolfram.com/images/eps-gif/Brick_1000.gif A perfect cuboid is a cuboid having integer side lengths, integer face diagonals http://mathworld.wolfram.com/images/equations/PerfectCuboid/Inline3.gif (1) http://mathworld.wolfram.com/images/equations/PerfectCuboid/Inline6....