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______ ．

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• 1. 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______ ．
• 2. 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______ ．
• 3. 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
• 4. Let n be a natural number, then three consecutive even numbers can be expressed as, three consecutive odd numbers can be expressed as, and three consecutive integers can be expressed as
• 5. It is known that a is the smallest natural number, B is the smallest odd number, M is the smallest even number except zero, C is the fraction, The numerator and denominator are B and m, respectively?
• 6. If there are five continuous natural numbers, and their sum can be expressed as the product of two continuous odd numbers which are all greater than 5, then the smallest of the five continuous natural numbers
• 7. Try to explain that the sum of the product of four integers and 1 is a complete square number
• 8. It is proved that the product of k consecutive positive integers is not a complete square number
• 9. Is the sum of the product of four continuous positive integers and 1 necessarily a complete square? Proof + example,
• 10. Try to prove that the product of four continuous positive integers plus 1 must be a complete square? (write the proof and steps)
• 11. 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}?
• 12. 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
• 13. Given that N2 + 5N + 13 is a complete square number, then the value of natural number n is______ ．
• 14. 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?
• 15. How many squares are there in a natural number with a single digit of 8 Please, it's about human life
• 16. In natural numbers with a single digit of 2, there are______ A square number
• 17. The square of a natural number is a four digit number, the thousand digit number is 4, and the five digit number is 5______ ．
• 18. 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___
• 19. Please prove that for any n natural numbers, one or the sum of several numbers must be a multiple of n
• 20. 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?