Can x-y Be Even While x²-xy+3 Is Odd?

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Discussion Overview

The discussion revolves around the mathematical problem of whether the expression x-y can be even while the expression x²-xy+3 is odd. Participants explore the implications of these conditions and attempt to clarify the relationships between the variables involved.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about how to approach the problem, indicating a lack of understanding of the requirements.
  • Another participant provides an example where x=7 and y=2, noting that x-y=5 is not even and x²-xy+3=38 is not odd, suggesting that the initial conditions may not hold true.
  • This same participant argues that if x-y is even, then x²-xy+3 can be expressed as x(x-y)+3, and they propose a proof that if 2 divides (x-y), then 2 also divides x(x-y), leading to a remainder of 1 when dividing x²-xy+3 by 2, thus making it odd.
  • There is no further elaboration or resolution provided in the thread, as it is closed for moderation.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the problem, as the discussion is interrupted by moderation and does not allow for further exploration of the claims made.

Contextual Notes

The initial post lacks effort in problem-solving, which may have influenced the responses and the decision to close the thread. The mathematical steps and assumptions involved in the claims remain unresolved.

bronx
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How to do this type of problem. I am confused, right now.
Prove that x-y is even and x2-xy+3 is odd
 
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##7-2=5## is not even and ##7^2 - 7*2 + 3 =38## is not odd.
However, if ##x-y## is even, then ##x^2 - xy + 3 = x(x-y)+3## is odd.
Proof: If ##2|(x-y)## then ##2|x(x-y)## and dividing ##x^2 - xy + 3 = x(x-y)+3## by ##2## has a remainder ##1##.
 
Thread closed for Moderation...
 
Thread will remain closed. Just a reminder, when you see misplaced schoolwork/homework type questions in the general math forums (especially when the OP shows zero effort to solve the problem), please Report the post rather than responding. Thanks.
 

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