Yang Hui Triangle is a triangular numerical table arranged by numbers, and its general form is as follows:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 2 1 35 35 2 1 7 1
… … … … …
The most essential feature of Yang Hui Triangle is that its two hypotenuses are all composed of the number 1, and the other numbers are equal to the sum of the two numbers on its shoulders. In fact, ancient mathematicians in China were far ahead in many important mathematical fields. The history of ancient mathematics in China once had its own glorious chapter, and the discovery of Yang Hui's triangle was a wonderful one. Yang Hui was born in Hangzhou in the Northern Song Dynasty. In his book "Detailed Explanation of Algorithms in Nine Chapters" written by 126 1, he compiled a triangle table as shown above, which is called an "open root" diagram. And such triangles are often used in our Olympic Games. The simplest thing is to ask you to find a way. Now we are required to output such a table through programming.
Odd number * odd number = odd number
Odd+even = odd
Odd+odd = even
Odd even number = even number
Even number+even number = even number
Even number * even number = even number
Silence is better than sound.
There is no lack of artistic conception in mathematics that silence is better than sound. 1903, at a mathematics report meeting in new york, mathematician Le Ke stepped onto the platform. He didn't say a word, but wrote down the calculation results of two numbers on the blackboard with chalk. One is the 67th power of 2- 1, and the other is19370721× 7665438+. Why is this?
Because Lecco has solved the problem that has been unclear for 200 years, that is, 2 is the power of 67-is1a prime number? Since it is equal to the product of two numbers, it can be decomposed into two factors, thus proving that 2 is the power of 67-1is not a prime number, but a composite number.
Cole only gave a short silent report, but it took him three years to reach a conclusion on all Sundays. The courage, perseverance and hard work contained in this simple formula are more attractive than the voluminous report.