May I get a comment on this proof?

  • Thread starter Thread starter flyingpig
  • Start date Start date
  • Tags Tags
    Proof
Click For Summary

Homework Help Overview

The problem involves proving a statement about the properties of integers, specifically relating to the expressions \(2^{2x}\) and \(4^{x}\). The original poster is tasked with demonstrating that if \(2^{2x}\) is an odd integer, then \(4^{x}\) must also be an odd integer.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to establish a direct proof by equating \(2^{2x}\) with \(4^{x}\) and questions the validity of this assumption. Other participants engage by affirming the correctness of the mathematical identity used.

Discussion Status

The discussion includes affirmations of the original poster's approach, with some participants expressing reassurance about the triviality of the concepts involved. However, there is no explicit consensus on the proof's completeness or correctness.

Contextual Notes

The original poster expresses uncertainty about the assumptions made in their proof, indicating a potential lack of clarity regarding the properties of the expressions involved.

flyingpig
Messages
2,574
Reaction score
1

Homework Statement



Prove directly:

Prove that if [tex]2^{2x}[/tex] is odd integer, then [tex]4^{x}[/tex] is odd integer


The Attempt at a Solution



[tex]2^{2x} = 2k + 1[/tex] for some k is integer

[tex]2^{2x} = 4^{x} = 2k + 1[/tex]

Thus completes the proof?

Am I allow to make the assumption (fact) [tex]2^{2x} = 4^{x}[/tex]?

Thanks
 
Physics news on Phys.org
That is correct. It is indeed true that [itex]a^{bc}=(a^b)^c[/itex].
 
nvm...I am just being an idiot
 
That's okay, sometimes I get concerned when things are trivial too.
 

Similar threads

Replies
7
Views
4K
  • · Replies 12 ·
Replies
12
Views
7K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 105 ·
4
Replies
105
Views
11K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 14 ·
Replies
14
Views
2K
  • · Replies 4 ·
Replies
4
Views
1K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
5
Views
2K
Replies
3
Views
3K