Try to explain that the sum of the product of four integers and 1 is a complete square number

RELATED INFORMATIONS

• 1. It is proved that the product of k consecutive positive integers is not a complete square number
• 2. Is the sum of the product of four continuous positive integers and 1 necessarily a complete square? Proof + example,
• 3. Try to prove that the product of four continuous positive integers plus 1 must be a complete square? (write the proof and steps)
• 4. 1. The sum of the product of four consecutive integers and 1 is a complete square number. Why? Please explain the reason 2. Simplification (2 - M + 2-2 * 2 - n) / 2 * (2 - N + 3) 3. Factorization (1) (x - 2 + Y - 2) - 4x - 2 * y - 2 (2) 4*（a+b)⌒2-4*(a+b-1/4)
• 5. Help me out a three digit divided by two digits {divisible, and must be divisible} formula, not less than 100, thank you Fourth grade pupils do the problem, must divide, good I give points, and a lot of Oh!
• 6. Let n be a natural number, then the odd number is expressed as______ , even numbers expressed as______ The number divisible by 5 is______ The number of 3 divided by 4 is______ ．
• 7. N is an integer, and N is used to represent the following numbers: odd number, even number, multiple of 5, number divisible by 3, three consecutive integers, integer divisible by 5 and 1 N is an integer, and n denotes the following numbers: Odd numbers, even numbers, multiples of 5, numbers divisible by 3, three consecutive integers, integers divisible by 5 and 1
• 8. If an integer can be divided by two and three, then the number can be divided by two____ to be divisible by?
• 9. At 0, 1, 2, 3 Of the 101 integers, 100, there are () A. 85 B. 68 C. 34 D. 17
• 10. In 0,1,2 ···, 100, how many numbers are divisible by 2 and 3 at the same time? Two two digit numbers, their greatest common divisor is 8, and their least common multiple is 96. The sum of these two numbers is ()
• 11. 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
• 12. 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?
• 13. 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
• 14. 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
• 15. 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______ ．
• 16. 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______ ．
• 17. 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______ ．
• 18. 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}?
• 19. 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
• 20. Given that N2 + 5N + 13 is a complete square number, then the value of natural number n is______ ．