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?

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• 1. Please prove that for any n natural numbers, one or the sum of several numbers must be a multiple of n
• 2. 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___
• 3. The square of a natural number is a four digit number, the thousand digit number is 4, and the five digit number is 5______ ．
• 4. In natural numbers with a single digit of 2, there are______ A square number
• 5. How many squares are there in a natural number with a single digit of 8 Please, it's about human life
• 6. 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?
• 7. Given that N2 + 5N + 13 is a complete square number, then the value of natural number n is______ ．
• 8. 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
• 9. 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}?
• 10. 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______ ．
• 11. 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?
• 12. 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
• 13. 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______ ．
• 14. It is proved that if n > 0, D divides 2n ^ 2, then n ^ 2 + D is not a complete square number
• 15. 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
• 16. 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?
• 17. If n is an integer, use a formula containing N: even numbers can be expressed as______ The odd number can be expressed as______ ．
• 18. N is an integer, and an algebraic expression containing N is used to express that two consecutive odd numbers are integers______ Two consecutive even numbers are______ ．
• 19. If the letter N is used to represent an integer, then the odd number is () and the even number is ()
• 20. For the natural number 1,2,3,..., n has 1 & sup3; + 2 & sup3; + 3 & sup3; +... + n & sup3; = [n (n + 1) / 2] & sup2;, that is 1 & sup3; + 2 & sup3+ For this equation, we propose a question, if the sequence {an}, has an > 0, and satisfies the equation (A1 & sup3; + A2 & sup3; +. + an & sup3;) = (a1 + A2 + a3 +.. + an) & sup2;, is an = n tenable? If it is tenable, prove it; otherwise, give a counter example