如果两个数 a 和 b 是奇数，则证明它们的和 a + b 是偶数
早期，先民不懂数数，习惯用符号和字母来表示不同的物体。后来他们用数字来表示事物，从而形成了数字系统。今天，如果一个人可以计算事物，那么由于数字系统，这可能是可能的。进一步的数字系统分为不同的子部分，例如十进制数字系统，二进制数字系统，八进制数字系统，十六进制数字系统。十进制数系统根据其特性包含不同类型的数字，例如自然数，整数，整数，有理数，无理数等。整数中有偶数和奇数，让我们了解偶数，
奇数
整数范畴中除偶数外的所有数字都是奇数。奇数是不能被 2 整除的数字，例如 5、7、9 等。所有这些数字在被 2 整除时都会留下一个数字 1 作为余数。
如果一个数能被 2 整除，余数为 0，则该数称为偶数。偶数是整数的子集。偶数的连续+2或-2也是偶数。偶数的示例有 -6、-8、10、6 等。0 也是偶数，因为当 0 除以 2 时，余数为 0。
如果两个数 a 和 b 是奇数，则证明它们的和是偶数。
证明：
If ‘a’ and ‘b’ are odd numbers it means that the remainder of a ÷ 2 will be one and similarly b is also an odd number so the remainder of b ÷ 2 will also be one.
The remainder of (a ÷ 2) = 1
The remainder of (b ÷ 2) = 1
Now to prove that remainder of (a + b) is also one, divide it by 2 then we can say that a + b is also an odd number.
Divide (a + b) by 2.
= (a + b) ÷ 2
By using distributive property, (x + y) ÷ z = (x ÷ z) + (y ÷ z)
= (a ÷ 2) + (b ÷ 2)
As discussed the remainder of (a ÷ 2) and the remainder of (b÷2) is zero. So it can be concluded that the remainder of (a ÷ 2) +(b ÷ 2) will be 1 + 1, i.e. 2, and since 2 is itself completely divisible by 2, the final remainder will again be 0.
Divide a + b by 2, the remainder is 0 and it fulfills the condition of an even number so can say that a + b is an even number.
类似问题
问题 1：如果 4 和 6 是偶数，那么证明它们的和也是偶数。
解决方案：
Divide a number by 2 and get 0 as remainder then that number is known as an even number.
Divide 4 by 2, we got 2 as the quotient and 0 as the remainder.
Divide 6 by 2 we got 3 as the quotient and 0 zero as the remainder.
The summation of 4 and 6 is 10.
Divide 10 by 2, it is gotten 5 as quotient and 0 as remainder. So it can be concluded that 10 is also an even number.
Hence proved, the summation of two even numbers is also an even number.
问题 2：证明 -6 和 2 的和是偶数。
解决方案：
Divide a number by 2 and got 0 as remainder then that number is known as an even number.
Divide -6 by 2 we got -3 as quotient and 0 as remainder.
Divide 2 by 2, we got 1 as the quotient and 0 as the remainder.
Sum of -6 and 2,
= (-6) + (2)
= -6 + 2
= -4
When we divide -4 by 2, we got 0 as the remainder so -4 is an even number.