Observe the following equation: 1 & sup2; - 0 & sup2; = 1,2 & sup2; - 1 & sup2; = 3,3 & sup2; - 2 & sup2; = 5,4 & sup2; - 3 & sup2; = 7 With the natural number n

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• 1. 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
• 2. If the letter N is used to represent an integer, then the odd number is () and the even number is ()
• 3. 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______ ．
• 4. If n is an integer, use a formula containing N: even numbers can be expressed as______ The odd number can be expressed as______ ．
• 5. 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?
• 6. 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
• 7. It is proved that if n > 0, D divides 2n ^ 2, then n ^ 2 + D is not a complete square number
• 8. 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______ ．
• 9. 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
• 10. 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?
• 11. A is a non-zero natural number. In the following formula () has the largest number, a divided by one tenth, four tenths multiplied by a, and a divided by five fourths. Why
• 12. A is a non-zero natural number. The largest number in the following formula is? A: 2 / 5 B. a multiplied by 2 / 5 C. A is 7 / 5
• 13. A is a non-zero natural number. The largest number in the following formula is () A. A × 3 / 4 B.A △ 3 / 4 C.A △ 1 and 1 / 3
• 14. A is a non-zero natural number, the largest of which is 1. Ax 3 / 4 2. Ax1 3. A ／ 1 4. A ／ 3 / 4
• 15. The product of natural number a multiplied by 168 is a complete square number, and the minimum value of a is obtained
• 16. Let the square number y ^ 2 be the sum of 11 consecutive positive integers, and find the minimum value of the positive integer y
• 17. a. B is a non-zero natural number, a is not equal to B, 90a + 102b is just a complete square number, find the minimum value of a + B
• 18. If the product of natural number a multiplied by 2376 is the square of natural number B, then a is the smallest______ ．
• 19. It is proved that if the limit of sequence xn is a, then for any natural number k, the limit of sequence xn + k is a
• 20. It is proved that n continuous natural numbers can be divided by 1x2x3x4x.xn