# Prove the following:For any natural number n, if n2 6n is an even number, then n is an even number.-You will use Overleafto typeset your solutions to the assignment andthen upload the file to

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Define an integer k to be odd if k − 1 is even. Write up a formal proof of the following, using an indirect proof:

Claim: For any natural numbers m and n, if m is odd and n is odd, then m + n is even. help_outlineImage TranscriptioncloseProve the following: For any natural number n, if n2 6n is an even number, then n is an even number. - You will use Overleaf to typeset your solutions to the assignment and then upload the file to fullscreen
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Step 1

Consider the following information and prove the following: help_outlineImage Transcriptionclosefor any natural number n, if n' +6n is an even number then n is an even number fullscreen
Step 2

Prove the above result by contradiction:

Since, if n2+6n is an even number then n is an even number.

Let’s ... help_outlineImage Transcriptionclosen26n (2k 1) +6(2k +1) = 4k2 +1+4k +12k +6 =2(2k 8k +3) +1 where, 2k 8k+3= p, p is any integer =2p+1 fullscreen

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