The square of a natural number is a four digit number, the thousand digit number is 4, and the five digit number is 5______ ．

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• 1. In natural numbers with a single digit of 2, there are______ A square number
• 2. How many squares are there in a natural number with a single digit of 8 Please, it's about human life
• 3. One 3-digit number is exactly 9 times of the other 3-digit number. How many pairs of 3-digit numbers are there in a natural number?
• 4. Given that N2 + 5N + 13 is a complete square number, then the value of natural number n is______ ．
• 5. Natural number n is a complete square number after adding line 2, and it is also a complete square number after subtracting 1. It is proved that natural number n satisfies the condition 4n-n ^ 2-3 > 0
• 6. The formula "1 + 2 + 3 + 4 +..." +"100" represents the sum of 100 consecutive natural numbers starting from 1, It is inconvenient to write. For the sake of simplicity, we express it as ∑ (100 above, n = 1 below, and N on the right). Here the ∑ is the summation sign. Through reading the above materials, we can calculate ∑ {012 above, n = 1 below, and 1 / n (n + 1) on the right}?
• 7. Observe the following equations: 12-02 = 1; 22-12 = 3; 32-22 = 5; 42-32 = 7 Let's use an equation with natural number n to show that the law you find is______ ．
• 8. If there is a natural number whose sum with 160 is equal to the square of a certain number, and whose sum with 84 is equal to the square of another number, then the natural number is______ ．
• 9. Observe the following equations: 4-1 = 3, 9-4 = 5, 16-9 = 7, 25-16 = 9, 36-25 = 11 Let n be a natural number, and let n be an equation containing n______ ．
• 10. 3. Let n be a natural number, then the odd number is (), the even number is (), and the three consecutive natural numbers are（ 3. If n is a natural number, then the odd number is () and the even number is () and the three consecutive natural numbers are () 4. If the chickens and rabbits are in the same cage, m chickens and N rabbits, there are () heads and () feet in total. 5. Greening a piece of land with a 5-person team can be completed in M days. Greening this piece of land with an 8-person team can be completed in () days
• 11. If the square of a natural number is a four digit number, a thousand digit number is a word, a four digit number, and a five digit number, then the natural number is a four digit number___
• 12. Please prove that for any n natural numbers, one or the sum of several numbers must be a multiple of n
• 13. There are three continuous natural numbers. The sum of the square difference of the larger and smaller numbers and the middle natural number must be a multiple of () There is an option in the multiple choice question, a = 0?
• 14. Let n be a natural number, and try to explain that the square difference between N + 5 and n-3 must be a multiple of 16?
• 15. There is a natural number, it adds 1 is a multiple of 2. Add 2 is a multiple of 3, add 3 is a multiple of 4, add 4 is a multiple of 5, add 5 is a multiple of 6, add 6 is a multiple of 7, then why add 0 after 2 * 3 * 4 * 5 * 6 * 7? It's 1, not 0. Wrong number
• 16. There is such a natural number: it adds 1 to be a multiple of 2, adds 2 to be a multiple of 3, adds 3 to be a multiple of 4, and adds 4 to be a multiple Five times, plus five is a multiple of six, plus six is a multiple of seven, in this natural number, except for one, the smallest is______ ．
• 17. It is proved that if n > 0, D divides 2n ^ 2, then n ^ 2 + D is not a complete square number
• 18. If n is a natural number and any even or odd number is represented by a formula containing N, then even number is odd number and even number is odd number when n = 5
• 19. An integer that can be divided by two is called an even number, and an integer that cannot be divided by two is called an odd number?
• 20. If n is an integer, use a formula containing N: even numbers can be expressed as______ The odd number can be expressed as______ ．