Question

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1) If a and b are two odd positive integers such that a > b, then prove that one of the two numbers a+b/2 and a-b/2 is odd and the other is even.

2) Show that the square of an odd positive integer is of the form 8q + 1, for some integer q.

3) Prove that it is a positive integer is of the form 6q + 5, then is it of the form 3q + 2 for some integer q , but not conversely.

4) Prove that the product of three consecutive positive integer is divisible by 6.




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Plzz explain all 4 questions properly


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Answer 1

Hey!

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Answers are in the pics.

[Sorry if you don't understand my handwriting :P ]

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Hope it helps...!!!

Answer 2

Heya user☺☺

Refer to this attachment for the solution.

Hope it will help you☺☺