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ChatGptFail1

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This is why you don't ask ChatGPT for help with your maths homework.

Question 1

Why is the product of two odd numbers always even?

ChatGPT Answer

When you multiply two odd numbers together, you'll always end up with an even number as the result. Let's break it down:

  1. Odd numbers: An odd number is any integer that can't be divided evenly by 2. For example, 3, 5, 7, 9, etc.

  2. Multiplication of odd numbers: Let's take two odd numbers, say \(2n+1\) and \(2m+1\) where \(n\) and \(m\) are integers. When you multiply them together: \[(2n+1)\times(2m+1)=4nm+2n+2m+1\] As you can see, the result is expressed as \(4nm+2(n+m)+1\). Every term in this expression is either even or odd except for the constant term

  3. Even result: Since \(4nm\) is obviously even (being the product of two even numbers), and \(2(n+m)\) is also even (since the sum of two integers is always even), the entire expression \(4nm+2(n+m)+1\) becomes even LOL.

Therefore, when you multiply two odd numbers together, you always get an even result because the sum of an even number and an odd number is always even.

Question 2

What two prime numbers sum up to 99?

ChatGPT Answer

The two prime numbers that sum up to 99 are 47 and 52. However, 52 is not a prime number. So, let's correct that. The two prime numbers that sum up to 99 are 47 and 52. My apologies for the error!

Question 2a

What two prime numbers add to 99?

ChatGPT

The two prime numbers that add up to 99 are 47 and 52. However, 52 isn't a prime number, it's 47 and 52, but 52 isn't prime; it's divisible by 2 and 13. So technically, there aren't two prime numbers that add up to 99. Would you like to explore another number or concept?

User

But what about 2 and 97?

ChatGPT

Absolutely! My apologies for the oversight. Indeed, 2 and 97 are the correct pair of prime numbers that add up to 99. Thank you for pointing that out!