如果两个数 a 和 b 是偶数，则证明它们的和 a + b 是偶数
数字系统是一种以某种方式使用符号和数字来表示数字的系统。你可以把它想象成一本数学语法书。一旦我们听到“数字”这个词 1,2,3,...... 立即在我们脑海中浮现。数字系统定义了它们的值、要执行的操作和其他属性。
数字类型
每个号码都是独一无二的。它有很多变化。因此，它可以被认为是自然数、整数、偶数、奇数、素数、合数等。
- 自然数 - 它包含从 1 开始的数字。
- 整数 - 它包含从 0 开始的数字。
- 偶数——能被 2 整除的数。
- 奇数——不能被 2 整除的数。
- 素数——只能被 1 和自身整除的数字。即只有两个因素
- 合数 – 能被 1 和自身和其他数整除的数。即两个以上的因素
偶数
那些是 2 的倍数的数称为偶数。例如 2, 4, 6, 8, 10, ... 等等。这些数字可以分成两个相等的组或对。奇数不能分成相等的数。让我们试着理解它，number 1st group 2nd group Equality 2 1 1 yes 4 2 2 yes 6 3 3 yes 8 4 4 yes
因此，偶数可以平分。让我们简要地看一下偶数的一些重要性质。
偶数的一些性质
- 两个偶数之和总是偶数。
| num1 | num2 | num1+num2 |
|---|---|---|
| 2 | 8 | 10 |
| 12 | 16 | 28 |
- 两个奇数之和总是偶数。
| num1 | num2 | num1+num2 |
|---|---|---|
| 5 | 5 | 10 |
| 7 | 9 | 16 |
- 当偶数和奇数相乘时，结果总是偶数。
| num1 | num2 | num1 × num2 |
|---|---|---|
| 9 | 8 | 72 |
| 3 | 6 | 18 |
- 当偶数除以 2 时，余数始终为零。
| num1 | num2 | remainder of num1 ÷ num2 |
|---|---|---|
| 12 | 2 | 0 |
| 80 | 2 | 0 |
如果两个数 a 和 b 是偶数，则证明它们的和 a + b 是偶数
解决方案：
Suppose,
a = 2 × X
b = 2 × Y
where X and Y are any integers that may be even or odd. Multiplying any number by 2 is always even so 2X and 2Y are even.
a + b = 2 × X + 2 × Y = 2 × (X + Y)
The result has a factor of 2. So, it is always even.
Example:
Input: a = 2, b = 4
Output: a + b = 2 + 4 = 6 = 2 × 3
Hence, it is even.
类似问题
问题 1：如果两个数 a 和 b 是偶数和奇数，那么它们的和 a + b 是奇数。
解决方案：
Suppose,
a = 2 × X
b = 2 × Y + 1
where X and Y are any two integers.
a + b = 2 × X + 2 × Y + 1 = 2 × (X + Y) + 1
The result is similar to b which is an odd number. Hence, it is odd.
Example:
Input: a = 4
Input: b = 7
Output: a + b = 4 + 7 = 11
Hence, it is odd.
问题 2：如果两个数 a 和 b 是奇数，那么它们的和 a + b 是偶数。
解决方案：
Suppose,
a = 2 × X + 1
b = 2 × Y + 1
where X and Y are any two integers
a + b = 2 × X + 1 + 2 × Y + 1 = 2 × X + 2 × Y + 2 = 2 × (X + Y + 1)
Which is a factor of 2, so it is even.
Example:
Input: a = 3
Input: b = 5
Output: a + b = 3 + 5 = 8
Hence it is even.
问题3：两个素数a和b之和是多少？
解决方案：
All the prime numbers are odd except 2 which is even.
Hence, it is concluded that the addition of any two prime numbers is always even if we ignore 2.
First argument:
a = even i.e. 2
b = odd
a + b = even + odd = odd (from property)
Hence, it is odd.
Second argument:
a = odd
b = odd
a + b = odd + odd = even (from property)
Hence, it is even.
问题 4：有哪些不同类型的数字系统？
解决方案：
There are four types of number Systems,
1. Binary Number System
This number system contains the digits or numbers having base 2 i.e. only 0 and 1. For example, 10012 is a binary number.
2. Octal Number System
This number system contains the digits or numbers starting from 0 to 7 and has a base 8. For example, 2428 is an octal number.
3. Decimal Number System
This number system contains the digits or numbers starting from 0 to 9 and has a base of 10. For example, 102410 is a decimal number.
4. Hexadecimal Number System
This number system contains the digits or numbers starting from 0 to 15 and has a base of 16.
A – 10
B – 11
C – 12
D – 13
E – 14
F – 15
For example, A45B16 is an hexadecimal number.