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A natural number, it plus L is a multiple of 2, its two times plus 1 is a multiple of 3, its three times plus 1 is a multiple of 5______ ．
Let this natural number be x, then x + 1 = 2K, 2x + 1 = 3M, 3x + 1 = 5N. From the above formula, we can see that x is an odd number. If n = 2, x = 3, then 2 × 3 + 1 is a multiple of 3, so it is not suitable. If n = 5, x = 8, 8 are even numbers, so n = 8, x = 13, 13 × 2 + 1 = 27 is a multiple of 3, and 13 + 1 = 14 is a multiple of 2
There are natural numbers like this: 1 is a multiple of 2, 2 is a multiple of 3, 3 is a multiple of 4, 4 is a multiple of 5, 5 is a multiple of 6, and 6 is a multiple of 7. In this kind of natural number, the smallest number is 1______ ．
4 = 2 × 2, 6 = 2 × 3, so the least common multiple of 2, 3, 4, 5, 6, 7 is: 2 × 6 × 5 × 7 = 420420 + 1 = 421; so this number is 421. So the answer is: 421
The sum of a natural number and 3 is a multiple of 5, and the difference between a natural number and 3 is a multiple of 6______ ．
Let X be x, then x − 3 = 6nx + 3 = 5Z, N and Z are natural numbers, ｜ x = 6N + 3 and x = 5z-3, ｜ 5Z = 6 (n + 1), when n = 1, 5Z = 12, z = 125 is not the problem; when n = 2, 5Z = 18, z = 185 is not the problem; when n = 3, 5Z = 24, z = 245 is not the problem; when n = 4, 5Z = 30, z = 6 is the problem. So x = 4 × 6 + 3 = 27. So the answer is: 27
RELATED INFORMATIONS
- 1. A natural number plus 1 is a multiple of 2.3.4.5.6.7 A natural number, plus 1, is a multiple of 2 Plus one is a multiple of three Plus one is a multiple of four Plus one is a multiple of five Plus one is a multiple of six Plus one is a multiple of seven What's the number?
- 2. For three continuous natural numbers, the sum of the square difference of the larger and smaller numbers and the middle natural number must be the multiple of that number? 1,3,4,5
- 3. Take any 11 numbers from 1 to 20 and prove that there must be two numbers, one of which is a multiple of the other
- 4. SOS, known a four digit, thousands, hundreds, tens, and is the complete square of a natural number! Please use C + + program to calculate the number! (in fact, 7744!)
- 5. The sum of two natural numbers is 9858. The larger number is equal to the smaller number after removing the single digits. What are the two numbers? One more question: in the sixth grade group, the number of boys accounted for 4 / 9 of the total number of the group. Later, seven boys were transferred in. At this time, the number of boys was just 3 / 5 of the total number of the group? Please, I'm stupid. I have a lot of questions to ask you. Can I help you? Thank you! Another question: there are 120 ball, divided into two classes, class 1 to 3 / 1 and class 2 to 2 / 1 equal, ask two classes each to several ball?
- 6. Read the formula "1 + 2 + 3 + 4 +..." 100 "is the sum of 100 consecutive natural numbers starting from 1 as follows It's 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 ∑ {20 above, n = 1 below, and 1 / n (n + 1) on the right}? What does n (n + 1) mean? I don't understand it at all,
- 7. The formula 1 + 2 + 3 + 4 +. + 100 represents the sum of 100 natural numbers starting from 1. Because the formula is relatively long, the writing is not square For the sake of simplicity, we will express it as ∑ (100 above, n = 1 below, N in the middle). Here is the summation sign. Through reading the above materials, we can calculate ∑ (2014 above, n = 1 below, 1 / N of n (n + 1) at the opening in the middle)
- 8. Let n be a natural number, and use the algebraic expression containing n to express: 1. Three consecutive integers; 2. Two adjacent even numbers; 3. Two adjacent odd numbers
- 9. In natural numbers, the smallest even number is (), and the smallest odd number is ()
- 10. There are five consecutive odd numbers whose product is 328 185. Find these five natural numbers
- 11. Let a and n be positive integers, and a divide by 2n ^ 2. Try to explain that n ^ 2 + A is not an answer before the square number,
- 12. Primary school mathematics defines "in the natural number, what can be divided by 2 is even, what cannot be divided by 2 is odd". Now it is stipulated that there are odd and even numbers in negative integers
- 13. Let n denote an integer, and use the formula containing n to denote: (1) any even number; (2) any odd number
- 14. A is a non-zero natural number. The largest number in the following formula is () A. A÷25B. A×25C. A÷125
- 15. A. B and C are all non-zero natural numbers. The following can show that the formula of a > b is () A.A △ 1 B.A / C1
- 16. A is a natural number greater than 0. The largest number in the following formula is () A is a natural number greater than 0. The largest number in the following formula is () A.A divided by four fifths B.A multiplied by four fifths C.A divided by one and four fifths
- 17. A is a non-zero natural number. The largest number in the following formula is () A.A × 3 / 5 B.A △ 3 / 5 C.A △ 8 / 5
- 18. Let the square number y ^ 2 be the sum of the squares of 11 consecutive integers, and find the minimum value of Y It's the sum of squares! It's not the sum of squares
- 19. It is proved by limit that if the limit of XN is a, then for any natural number k, the limit of XN + k is a
- 20. You mathematical experts help! Half, one third, two fifths, three eighths, five thirteenth, eight twenty-one fill out the last two