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How to prove whether any number can be divided by 3? Next I'll show you how to learn whether any number can be divided by 3 Example 1: can 456321 divide by 3? No, add up all its numbers and divide by 3. If the division is complete, then it can divide by 3. If the division is incomplete, then it can't divide by 3. 4 + 5 = 9, 9 + 6 = 15, 15 + 3 = 18, 18 + 2 = 20, 20 + 1 = 21. 21 can divide by 3, so 456321 can divide by 3 Example 2: can 86453 divide by 3? No, add up all its numbers and divide by 3. If it can divide completely, then it can divide by 3. If it can't divide completely, then it can't divide by 3. 8 + 6 = 14, 14 + 4 = 18, 18 + 5 = 23, 23 + 3 = 26.26, so 86453 can't divide by 3 I read the above paragraph on the Internet. I want to know how to prove this principle?
It is proved that if a number is ABCDE, then the number = a × 10000 + B × 1000 + C × 100 + D × 10 + e × 1 = a × (9999 + 1) + B × (999 + 1) + C × (99 + 1) + D × (9 + 1) + e × 1 = a × 9999 + B × 999 + C × 99 + D × 9 + (a + B + C + D + e) × 1a × 9999 + B × 999 + C × 99
It is proved that the 48th power-1 of 3 can be divided by numbers between 20 and 30
3^48-1=(3^24+1)(3^24-1)=(3^24+1)(3^12+1)(3^12-1)=(3^24+1)(3^12+1)(3^6+1)(3^6-1)=(3^24+1)(3^12+1)(3^6+1)(3^3+1)(3^3-1)
among
3^3-1=26
3^3+1=28
How many palindromes are there in the five digit number where the hundreds are 0? How many palindromes are there in the even number?
If five palindrome number is ab0ba, then a ≠ 0 can be taken as any number from 1 to 9, counting 9 kinds; B can be taken as any number from 0 to 9, counting 10 kinds;
Therefore, the number of palindromes whose hundreds are zero is 9 × 10 = 90;
The number of palindromes is 4 × 10 = 40;
If a is an even number and the number of hundreds is random, then the number of hundreds can be divided into 10 types from 0 to 9, and the number of palindromes is 4 × 10 × 10 = 400
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- 8. If a natural number reverses each number, it is still itself. This number is palindrome number, such as 606, 90509. How many palindromic numbers are there from 1 to 1000000? How to find them?
- 9. Find some English palindrome words (left and right symmetry)
- 10. 1. Write a function, whose function is to determine whether a number is palindrome number. (the so-called palindrome number is read from left to right and read from right to left is the same number, such as 101). Find such a number between 11 and 999, it is not only palindrome number, but also its square sum cube is palindrome number
- 11. The maximum number of five palindromes divisible by 101 Palindromes are positive integers like 36563 2002
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- 15. It is proved that no matter what number m is, the value of square-m of algebraic formula m is always greater than that of algebraic formula m-2
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