The proof of the conclusion that this number must be equal to 495 can be done by mathematical induction. We noticed the fact that any three digits can be expressed as 100x+ 10y+z, where x, y and z are integers. Then we consider the sum of all three digits, and we can draw a conclusion: if the sum of all digits of three digits is a multiple of 9, then this three digit must be equal to 495.
We can further refine the above conclusion: 1. 1 If the percentile of three digits is any integer between 1 and 9, and the sum of ten digits and single digits is a multiple of 9, then the three digits must be equal to 495.
For example, the hundredth digit of a three-digit number is 2, and the sum of ten digits and one digit is a multiple of 9, then this three-digit number must be equal to 495. This is because the sum of the digits of 495 is also a multiple of 9, so we can prove this conclusion according to the basic steps of induction.
The principle of digital black hole;
The unique decomposition theorem of 1, number: any positive integer can be uniquely decomposed into the product of several prime numbers. This theorem is the basis of digital black holes, because only when we can decompose numbers into prime numbers can we better understand and explore the mystery of digital black holes.
2. Principle of cyclic shift: Every number in the sequence of digital black holes is the result of cyclic shift. This means that no matter which positive integer we choose as the starting point, the final sequence is the same. The number of cyclic shifts depends on how many 2, 3 and 5 are in the prime factor of the starting number.
3. Power principle: In a digital black hole, any power number will be replaced by a fixed number. This principle can be used to produce a series of digital black holes.
For example, if we choose 6 as the starting number, the first number in the sequence is 6 squared, the second number is 8, the third number is 36, the fourth number is 484, and so on. This is because the square of 6 is equal to 36, and 36 can be decomposed into 2×2×3×3, so you can get 8; And 8 can be decomposed into 2×2×2, so you can get 484.