A question about odd and even numbers proves that the sum of an odd number and an even number is an

Reverse thinking: Suppose you have 21 small line segments, one is "good" and the other is "bad", connected into ropes with different colors at both ends, "good" cannot change color, "bad" can change color, then "bad" must be odd, (even numbers are reverted to the original color), "good" is an even number.

This kind of question: the "bad" must be odd.

The total number of segments is an odd number, and the "good" number is an even number; The total number of segments is even, and the "good" is odd.

Point A is colored red, point B is colored blue, and there is 1 "good" line segment at the beginning.

If there are x points with 2 points, then there are (20-x) points with 0 points.

Among the 21 line segments, there are"Okay" line segment = 1 + 2x + 0 * (20-x) = 2x + 1 is an odd number.

Good landlord

It is easy to know that when n is an odd number, the nth number is divisible by 3, such as 0, 3, 21, 144, 987....

Observe the next number of the above numbers, these numbers are like 1, 8, 55, 377, 2584...

The number greater than 6 is divided by 6 respectively.

From 8) the remainder is 2, 1, 5, 4, 3, 2, 1, 5, 4....

The rule is 5 to 1 five cycles, and there are more than 2 and 1 before the cycle

The position of 8 is the fourth of the number given in the question, and the number in the even order between the seventieth and the fourth is (70-4) 2+1=34 (pieces).

34-2) 5=32 5=6 remainder 2, where 34-2 is due to the fact that these numbers are first started and then cycled, and these two relatively irregular numbers must be subtracted before continuing).

In the cycle of 5 to 1, it is in the second place, which is 4

Therefore, the rightmost number is divided by 6 by 4...

This is really difficult to explain.

I think it might be confusing.

The calculations may be wrong, and they are absolutely correct in theory, and I hope that the main body of the building will do it.

From 501 to 599 there are 99 numbers in total.

Odd number = (1 + 99) 2 = = 50.

The remaining 49 are even.

Divide them into 50 odd numbers and add them up to 49 even numbers.

The sum of 49 even numbers is an even number.

The sum of 50 odd numbers is an even number [even number of odd numbers and the sum of even numbers] so even number + even number == even number.

Therefore, the sum from 501 to 599 is even.

Feel free to add it. The landlord has worked hard! ~~

It may be tomorrow.

1. Definition: Odd number refers to a number that is not divisible by 2, which is commonly known as a singular number. An even number is a number that is divisible by 2, which is commonly known as a double number.

2. Relationship: Integers can be divided into two categories: odd and even. Numbers that are divisible by 2 are called even numbers, and numbers that are not divisible by 2 are called odd numbers.

Even numbers can usually be represented by 2k (k is an integer), while odd numbers can be represented by 2k+1 (k is an integer). Note that because 0 is divisible by 2, 0 is an even number.

Proof: The expression of odd numbers is 2n+1, and the expression of even numbers is 2n, and the sum of odd and even numbers is 4n+1

Since 2n is an even number, 4n is also an even number.

So 4n+1 is an odd number, so the sum of an odd number of pants and an even number is an odd number.

As follows:

Odd x Odd = Odd.

Qi + Qi = Qi.

Even + Even = Even.

Odd + Even = Non-Odd and Non-Even.

Odd x Even = Odd.

Even x Even = Even.

Regarding even and odd numbers, there are the following properties:1) Two consecutive integers must be an odd number and an even number.

2) The sum or difference between odd numbers and odd numbers is an even mega number; The sum or difference between an even and an odd number is an odd number; The sum of any number of even numbers is even; The sum of singular odd numbers is odd; The sum of even odd numbers is even.

3) The sum or difference of two odd (even) numbers is even; The sum or difference between an even number and an odd number must be an odd number.

4) All positive and even numbers except 2 are composite.

5) The greatest common divisor of the adjacent even numbers of the clan is 2, and the multiple of the most auspicious minor common is half of their product.

1. In each of the following equations, there is at least one odd number and one even number, so how many even numbers are there among the 12 integers of Sun Limb?

= Family Rock = 2, arbitrarily take out 1234 Lian Zhaokai Imperial Continuation Natural Numbers, is their sum odd or even?

3. A string of numbers is arranged in a row, and their law is: the first two numbers are 1, and from the third number, each number is the sum of the first two numbers. Such as: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ,...

Just ask: How many even numbers are in the first 100 numbers (including the 100th number) of this string?

4. Can 1010 be written as the sum of 10 consecutive natural numbers? If you can, write it out; If not, explain why.

5. Is it possible to divide the 25 natural numbers from 1 to 25 into groups such that the numbers in each group are equal to the sum of the other numbers in the group?

6. In a chess match, the winner gets 1 point, the loser deducts 1 point, and if it is a draw, both sides get 0 points. There are a number of students competing today, and each of them is playing a game. One of the students scored a total of 7 points and the other student scored 20 points, indicating that there was at least one draw in the course of the game.

7. Write 1,2 ,... on the blackboard, 909, as long as there are two or more numbers on the blackboard, erase any two of the numbers a, b, and write a-b (where a b). Q: Is it odd or even left on the board at the end?

8. Set A1, A2 ,..., a64 is the natural number 1,2,..., 64, so that b1=a1-a2, b2=a3-a4,...，b32=a63-a64;c1=b1-b2，c2=b3-b4，…，c16=b31-b32;d1=c1-c2，d2=c3-c4，…，d8=c15-c16;……

If you keep doing this way, will you end up with an odd or even integer?

The sum of odd and odd numbers is even, and the sum of odd and even numbers is odd, so the answer is: even; Odd