You can go through the path once.
This is closed.
Each edge has even links.
2018年2月28日水曜日
Eulerian trail
You need to go back the start point in Eulerian trail.
You can go through the path once.
This is closed.
Each edge has even links.
You can go through the path once.
This is closed.
Each edge has even links.
2018年2月9日金曜日
Perfect number
A perfect number is a number that is half the sum of all of its positive divisors, and it is including itself.
28 is the perfect number.
28=1 + 2 + 4 + 7 + 14
σ(28)=1 + 2 + 4 + 7 + 14 + 28 = 2*28 = 56
Euler proved that all even perfect numbers were in the Euclid–Euler theorem.
The sum of divisors of a number must include the number itself, not just the proper divisors.
σ(2^2(2^3-1))=σ(4)σ(7)=(1+2+4)(1+7)=7*8=56=σ(28)
This is known as Mersenne primes.
2(2^2-1)=6
2^2(2^3-1)=28
2^4(2^5-1)=496
These are perfect numbers.
3,7,31 are primes, so you can find perfect numbers infinitely because of fractal. However, odd perfect numbers are unknown.
σ(N)=2N
28 is the perfect number.
28=1 + 2 + 4 + 7 + 14
σ(28)=1 + 2 + 4 + 7 + 14 + 28 = 2*28 = 56
Euler proved that all even perfect numbers were in the Euclid–Euler theorem.
The sum of divisors of a number must include the number itself, not just the proper divisors.
σ(2^2(2^3-1))=σ(4)σ(7)=(1+2+4)(1+7)=7*8=56=σ(28)
This is known as Mersenne primes.
2(2^2-1)=6
2^2(2^3-1)=28
2^4(2^5-1)=496
These are perfect numbers.
3,7,31 are primes, so you can find perfect numbers infinitely because of fractal. However, odd perfect numbers are unknown.
登録:
投稿 (Atom)