Respondent Wang Yuan and
How to use the residual business method (answer 2)
The remainder business method is actually the most important part of the 1 mathematical problem, and the P (polynomial algorithm) problem is the NP (non-polynomial algorithm) problem.
"P (polynomial algorithm) problem versus NP (non-polynomial algorithm) problem" has four contents:
1 addend (the second addend of 1 addend) participates in determining the size of sum numbers, and can change the attributes of numbers: "The sum of numbers with the same attributes is even, and the sum of numbers with different attributes is odd." Polynomials and non-polynomials can be operated directly. 2. Subtraction and minuend (because it is a natural number operation, the minuend must be greater than subtraction) participate in determining the size of the difference, which can change the attribute of the number: "The difference of numbers with the same attribute is even, and the difference of different attributes is odd." Polynomials and non-polynomials can be operated directly. 3. Multiplier, which participates in determining the size of the product, can change the attribute of the number: "The product of 2 is even and the product of odd is odd." Polynomials and non-polynomials can be operated directly. 4. The divider only participates in determining the size of the quotient, and cannot change the attribute of the quotient; Nor can it determine the attributes of numbers. Polynomials and non-polynomials can be operated directly. Dividers not only participate in determining the size of quotients, but also determine the attributes of numbers through quotients. Only one number can be determined at a time, and polynomials cannot be directly operated because of their uncertain properties. Non-polynomials can be operated directly. The law of remainder is to determine the attribute of a number by quotient and divisor. See reply 1 for the judgment method. The congruence law is the most important part of the divisor problem of P (polynomial algorithm) compared with NP (non-polynomial algorithm).
Supplement: 0 is not divisible: 0 only occupies a certain number of digits, but does not represent a certain number; Unable to determine the properties of the number. Separable number requirements: the size of quotient and the attribute of number can be determined by quotient. None can be divided, so 0 can't be divided.
The proposition of Goldbach's conjecture is Goldbach's suggestion: the sum of two prime numbers is even-it is the change of the attribute of the number rather than the change of the quantity. As for "big" and "big enough", they are both conditions and attributes of prime numbers at this time. For example, Goldbach conjecture when approaching infinity refers to prime numbers when approaching infinity. Natural numbers have two concepts: the number of numbers and the attributes of numbers. The concept of modifying, limiting and stating the size of a number is called the number of numbers; What kind of number is modified, restricted and stated is called the attribute of number. The quantitative proposition of number cannot be proved by the attribute formula of number; Similarly, the attribute proposition of number cannot be proved by the formula of number. The nontrivial zeros of Goldbach conjecture and Riemann hypothesis (this conjecture refers to Riemann zeta function: zeta (s) = ∑ 1/ns (n from1to infinity) are all on the straight line of Re(s)= 1/2.
Riemannian zeta function
σ 1/n=( 1+ 1/2+ 1/2^2+...)( 1+ 1/3+ 1/3^2+...)( 1+ 1/5+ 1/5^2+...)......=π( 1- 1/p)^- 1。
Where n crosses all positive integers and p crosses all prime numbers. )
Are attribute propositions of numbers. At that time, Riemann also wanted to use the attribute formula to prove that "the sum of the reciprocal of prime numbers". Only the reciprocal sum of prime numbers is required, so that the prime numbers can be found and prime formula can be written. With prime formula, you can prove many math problems in the world! He doesn't know that "reciprocal of prime number" itself is an attribute concept, which can't be proved by quantitative formula. "Reciprocal sum of prime numbers":1/3+1/5+1/7+...+1/p, which has three shortcomings: 1. 1/3, 3 has two. 5 has four possible remainders 1, 2, 3, 4, 1/5, including only the possible remainders 1 of 5, excluding the other three possible remainders 2, 3 and 4 of 5; 7 has six possible remainders: 1, 2, 3, 4, 5, 6,1/7,7. All possible remainders have been included, so the calculated results will be imperceptible. At first glance, it is correct. Careful analysis is a quantitative operation. An attribute proposition that cannot prove a number. 2. Without using the most critical number of residual commercial law-"possible residual number", scattering will occur, and there is no result in the model. Using "possible remainder" to fix prime numbers in a certain range is the result of "convergence" With "possible remainder", I don't know how to change "quotient" into "quotient bit", because the attribute formula uses "quotient bit"; The quantity formula uses "quotient". The difference between "quotient" and "quotient position" is that "quotient" emphasizes not only the position and size of a single number, but also the number of integers, such as:1/7 = 0.142857 ...1; There is an 8 in it, the number is 8, the position is ten thousand, and everything else is counted. The total quantity is:1/7 = 0.142857 ...1.
"Business" is different. Only the number of individual numbers is emphasized, and the position and overall number are not emphasized.
For example, the quotient of 7 is 1/4/2.8/5/7. Don't recycle the rest. This is also the most mysterious number in the Egyptian pyramids:
142857. Egyptian pharaohs knew how to use Shangzhi more than 5000 years ago.
The actual practice is simple: as long as the quotient obtained by operation can be taken as an integer, no matter where it is.
Represented by "quotient", the quotient sum of 7 is: 1+4+2+8+5+7=27, or1+8+2+7+4+5 = 9+9 = 3 * 9 = 9/2×.
Using the quotient and 7, the formula of 7 can be deduced:
7=2/9×27+ 1=6+ 1=7.
By analogy, the prime number formula is:
Pn=2/9Sp+ 1。
In the same way, the even number formula can be derived: (only add the 1 bit after the decimal point).
En=2/9 (SE-5)+2
The odd number formula is the same as that of prime formula: (only add the 1 bit after the decimal point).
Pn=2/9Sp+ 1
Goldbach conjecture when approaching infinity (English version) was plagiarized by Indian mathematician Professor Rajarama Gandhi. Recommended by mathematician Professor Gupalakrishna, published in South Asian Journal of Mathematics. (After many efforts to recover. )
Riemann Hypothesis (English version) and Four-color Conjecture (English version) were published in South Asia Journal of Mathematics (published by myself).
The complete proof of Goldbach's conjecture (English version) and Goldbach's conjecture are only proved by complementary commercial law (English version) and published in the American Open Mathematics Journal.
1. Even number formula is:
2. The strange formula is:
3. prime formula is;
4. The formula of the number approaching infinity is
They all express only the attributes of numbers.