For any integer n, the following numbers or expressions can divide the square of the polynomial (n + 5) - where is the square of N It needs to be explained in detail

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• 1. Can you show that (n + 7) & sup2; - (N-5) & sup2; is divisible by 24
• 2. Let's introduce letters. The suitable algebra is: (1) an integer divisible by 3; (2) an integer whose remainder is 2
• 3. 1) It is proved that if a divides B × C, and a and B are coprime, then a divides C (ABC is an integer). If the theorem is wrong, give an example and modify it, and prove the modified theorem 2) It is proved that if a and B are positive integers, if a > b, then the square of a > the square of B, and vice versa
• 4. It is proved that no matter what number m is, the value of square-m of algebraic formula m is always greater than that of algebraic formula m-2
• 5. Polynomial. The difference between a polynomial and - 5Y & # 178; - 13y is - Y & # 178; + 3y-1 2. Given X-Y = 3, xy = 2, find the difference of (3y-2x + 2x + XY) - (- 5x + 6xy + 6y) 3. Given a = 2m & # 178; n-mn & # 178;, A-B = 0, find B
• 6. Any even number greater than 2 can be expressed as the sum of two prime numbers. How to prove?
• 7. Who can prove that the sum of two primes is even?
• 8. The maximum number of five palindromes divisible by 101 Palindromes are positive integers like 36563 2002
• 9. How to prove whether any number can be divided by 3? Next I'll show you how to learn whether any number can be divided by 3 Example 1: can 456321 divide by 3? No, add up all its numbers and divide by 3. If the division is complete, then it can divide by 3. If the division is incomplete, then it can't divide by 3. 4 + 5 = 9, 9 + 6 = 15, 15 + 3 = 18, 18 + 2 = 20, 20 + 1 = 21. 21 can divide by 3, so 456321 can divide by 3 Example 2: can 86453 divide by 3? No, add up all its numbers and divide by 3. If it can divide completely, then it can divide by 3. If it can't divide completely, then it can't divide by 3. 8 + 6 = 14, 14 + 4 = 18, 18 + 5 = 23, 23 + 3 = 26.26, so 86453 can't divide by 3 I read the above paragraph on the Internet. I want to know how to prove this principle?
• 10. How many palindromes are there in five digits
• 11. Nickname Theory: for any integer n, polynomial (4N * 2 + 5) * 2-9 can always be divided by 8
• 12. From 1 to 100, how many numbers can be divided by 2 or 3?
• 13. From 1 to 100, there are 34 numbers divisible by 5 and 7 Is a number that can be divided by 5 or 7
• 14. If a number can be divisible by two and three at the same time, it must be divisible by six______ ．
• 15. There are () odd numbers between 100 and 200, () even numbers, and () multiples of 5. The ones of 3 can be divided by 3 and 5 at the same time How many can be divided by 3 and 5 at the same time
• 16. If n is not a natural number, then all even numbers can be expressed as____ All odd numbers can be expressed as____ The number divisible by 5 can be expressed as___ The number 2 divided by 3 can be expressed as___ .
• 17. Divide four digits by two digits and divide 50 channels
• 18. A four digit number can be divided by two consecutive two digit numbers. If the four digit number is divided by one of them, the quotient is 141. If the four digit number is divided by the other, the quotient is larger than 141. The four digit number is 141
• 19. Is the proposition "the sum of the product of four continuous positive integers and 1 must be a complete square number"
• 20. There are four natural numbers which are not equal to each other. The difference between the maximum number and the minimum number is equal to 4. The product of the minimum number and the maximum number is an odd number, and the sum of these four numbers is the smallest two odd numbers. What is the product of these four numbers?