Yes, the sum of two odd numbers will always result in an even number.
Here's why:
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Definition of an Odd Number: An odd number can be represented as 2n + 1, where 'n' is any integer.
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Sum of Two Odd Numbers: Let's take two odd numbers, represented as 2n + 1 and 2k + 1 (where 'n' and 'k' are any integers). Their sum is:
(2n + 1) + (2k + 1) = 2n + 2k + 2
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Factoring out a 2: We can factor out a 2 from the sum:
2n + 2k + 2 = 2(n + k + 1)
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Even Number Result: Since the sum can be expressed as 2 multiplied by an integer (n + k + 1), the result is, by definition, an even number.
Example:
- Let's take the odd numbers 3 and 5.
- 3 + 5 = 8
- 8 is an even number.
In Summary:
When you add any two odd numbers together, the result will invariably be an even number. This is due to the fundamental properties of odd and even numbers.
