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Number Theory Level 1

The absolute difference between any two even numbers is always an even number.

Is it true that the absolute difference between any two odd numbers is always odd?

Yes No

2 solutions

Aditya Kumar
Apr 25, 2016

Relevant wiki: Even and Odd Numbers

Any odd number can be written in the form $2n+1$ , for any positive integral value of $n$ .

So we take two odd numbers $2a+1$ and $2b+1$ .

Therefore the absolute difference between them is $2(a-b)$ or $2(b-a)$ . Now we can see that the absolute difference is an integral multiple of 2.

Hence, we can conclude that the absolute difference between any two odd numbers is even.

Challenge Master Note: Great!

Pi Han Goh - 5 years, 1 month ago

Hahahahah. I feel you are the only non-staff member who could be eligible to use Challenge Master Note.

Aditya Kumar - 5 years, 1 month ago

Hahah? What? You can do it too!

Pi Han Goh - 5 years, 1 month ago

@Pi Han Goh – No way. I mostly attempt problems of calculus, number theory, algebra and physics. You cover all maths topics.

Aditya Kumar - 5 years, 1 month ago

@Aditya Kumar – That's a lot of topics already. You're pretty good yourself too! Don't sell yourself short! =D

Pi Han Goh - 5 years, 1 month ago

@Pi Han Goh – Yes. That boosts my confidence. Now I shall post a calc problem soon.

Aditya Kumar - 5 years, 1 month ago

Akash Patalwanshi
Apr 30, 2016

It is not the solution. Is the word 'absolute' is necessary? We already know difference between any two even numbers is even but, the difference between any two odd number is not odd. For example $5 - 3 = 2$ which is an even number.

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