If you take any five natural numbers, the sum of at least two natural numbers is even

Take any five natural numbers, which may be 1. All are even, the sum of any two are even, 2.4 even, 1 odd, in which the sum of any two even numbers must be even, 3.3 even, 2 odd, in which the sum of any two even numbers must be even, and the sum of two odd numbers is even, 4.2 even, 3 odd, in which the sum of any two odd numbers must be even, 2 even

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1. The product of any two continuous natural numbers must be () A. Prime B. composite C. odd D. even
2. For three consecutive natural numbers, the minimum number is a multiple of 15, the middle number is a multiple of 17, and the maximum number is a multiple of 19. What are the three natural numbers You must be right ample reward
3. Three consecutive natural numbers are between 100 and 200, the smallest of which can be divided by 3, the middle by 5, and the largest by 7. Try to write all these three natural numbers
4. Arrange the natural number 1 23 4 5 6 7 8 9 in turn and write it down repeatedly to form a 1999 digit. Can this number be divided by 9? Why? It's best to have specific instructions
5. In the following six digits, f is a natural number that is not equal to 0 and less than 10, s is 0, and the number that must be divisible by 3 and 5 is () A. FFFSFFB. FSFSFSC. FSSFSS
6. The following four numbers all represent six digits, where n represents 0 and M represents any natural number from 1 to 9. Which one must be divisible by 3 and 5 at the same time? A.mmnmmn B.mnnmnn C.mnmnmn D.mnnnnn
7. The natural numbers from 1 to 30 are divided into two groups, so that the product a of all numbers in the first group can be divided by the product B of all numbers in the second group. What is the minimum value of AB?
8. Please use mathematical induction to solve: prove: 3 ^ 2n-2 ^ 2n can be divided by 5 (n belongs to positive natural number)
9. The sum of the product of four continuous natural numbers and 1 must be the complete square of a certain natural number 1) Calculation: (x + 1) (x + 2) (x + 3) (x + 4) 2) In the above formula, X is taken as 0.1.2.3... (1) what are the characteristics of the sum of the value of the polynomial and 1?
10. A number is the continuous product of 5 2, 3 3, 2 5, 1 7. Of course, there are many divisors of this number which are two digits. Among these divisors, what is the largest?
11. "At least one of several continuous natural numbers is even" The wrong number is "at least one of the three consecutive natural numbers is even", which is proved by the drawer principle
12. At least one of any three consecutive natural numbers is even
13. If a number is multiplied by another two adjacent odd numbers, the difference between the two products is 100______ ．
14. If a natural number is multiplied by two adjacent even numbers and the difference between the products is 240, then the number is zero___ .
15. There is a kind of natural number, starting from the third number, each number is just the sum of the two numbers in front of it, such as 246 347, etc
16. What is the sum of these three natural numbers
17. The sum of two adjacent natural numbers is 101. How to solve these two natural numbers with the equation?
18. The sum of two adjacent natural numbers is 37. How many of these two natural numbers are solved by equation
19. The product of two natural numbers is 36, and the least common multiple is 120? This is what the book says. If it's not right, how can I change it?
20. Decomposition quality factor from 80 to 90