Square of Odd Integers & Justifying "If P2 Is Even, Then P Is Even

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Discussion Overview

The discussion revolves around demonstrating that the square of any odd integer is odd and using this fact to justify the statement "if p² is even, then p is also even." The scope includes mathematical reasoning and conceptual clarification related to properties of integers.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant suggests showing that the square of any odd integer is odd as a means to justify the statement regarding evenness of p² and p.
  • Another participant prompts for clarification on what has been attempted so far to identify where assistance may be needed.
  • A third participant provides a series of examples illustrating odd integers in the form of 2x + 1, demonstrating that these integers are odd through specific calculations.
  • A later reply states that (2x + 1) is odd and provides a mathematical expansion showing that (2x + 1)² results in an odd number, reinforcing the earlier claim.

Areas of Agreement / Disagreement

Participants appear to be exploring the properties of odd integers and their squares, but there is no consensus on the justification of the statement regarding evenness, as the discussion is still in progress.

Contextual Notes

The discussion does not resolve the implications of the initial statement about evenness, and the mathematical steps leading to the justification are not fully explored.

Who May Find This Useful

Readers interested in properties of integers, mathematical proofs, or those seeking clarification on odd and even number relationships may find this discussion relevant.

winsome
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show that the square of any odd integer is odd, use this fact to justify the statement "if p2
is even , then p is also even
 
Physics news on Phys.org
Well, what did you try already? If we know where you're stuck, then we'll know where to help...
 
A good first step is noticing that

...
-5 = 2*(-3) + 1
-3 = 2*(-2) + 1
-1 = 2*(-1) + 1
1 = 2*0 + 1
3 = 2*1 + 1
5 = 2*2 + 1
...
 
(2x+1) is odd. (2x+1)^2=4x^2+4x+1 but 4x^2+4x is even and even +1 gives odd.
So (2x+1)^2 is odd
 

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