- #1
Aditya89
- 23
- 0
If m^2<a<b, & a*b=a perfect square, TPT: b>(m+1)^2
Proving b>(m+1)^2 for Perfect Square Conditions
- Context: Graduate
- Thread starter Aditya89
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- Conditions Square
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Discussion Overview
The discussion centers around proving the inequality b > (m + 1)^2 under the conditions that m^2 < a < b and that the product a*b is a perfect square. The scope includes mathematical reasoning and potentially homework-related inquiry.
Discussion Character
- Exploratory, Homework-related, Mathematical reasoning
Main Points Raised
- One participant proposes the theorem to prove (TPT) that b > (m + 1)^2 given the conditions.
- Another participant questions the interpretation of a*b = a, suggesting it may not align with the intended meaning.
- A participant clarifies that a*b should be understood as a perfect square, specifically a*b = k^2 where k is a natural number.
- There is a suggestion to treat cases where "a" is a perfect square separately from cases where "a" is not a perfect square.
- One participant expresses difficulty in explaining their understanding of the problem clearly.
- A request for assistance in creating mathematical symbols in posts is made.
- Another participant provides guidance on how to create mathematical symbols using LaTeX and suggests looking for a sticky post on the topic.
Areas of Agreement / Disagreement
Participants do not appear to have reached a consensus on the interpretation of the conditions or the approach to the proof, indicating multiple competing views and unresolved aspects of the discussion.
Contextual Notes
There are limitations in clarity regarding the definitions of terms used, particularly the conditions surrounding a and b, and the mathematical steps involved in the proof remain unresolved.
Who May Find This Useful
Readers interested in mathematical proofs, particularly in the context of inequalities and perfect squares, may find this discussion relevant.
- #2
shmoe
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a*b=a means a is zero or b=1?? This is surely not what you mean?
What does TPT mean? "To Prove True"?
What does TPT mean? "To Prove True"?
- #3
shmoe
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Huh, on furthur reflection I guess "& a*b=a perfect square" means "and a*b is a perfect square".
Is this a homework problem? In case it is, just a simple hint for now- treat the cases where "a" is a perfect square and "a" is not a perfect square separately.
Is this a homework problem? In case it is, just a simple hint for now- treat the cases where "a" is a perfect square and "a" is not a perfect square separately.
- #4
armandowww
- 76
- 0
I've understood the trouble... and I've got my picture but I think that I can't explain in a simple way... in sense that I'm not able to make it easy...
- #5
Aditya89
- 23
- 0
Sorry for the confusion!
Sorry, a*b= k^2, k belongs to the naturals. Not that a*b=a. Really sorry!
Thanks for the hint, Shmoe! I may be clser to the solution by an another method. I'll let you know if I get it. BTW, TPT is "to prove that".
Sorry, a*b= k^2, k belongs to the naturals. Not that a*b=a. Really sorry!
Thanks for the hint, Shmoe! I may be clser to the solution by an another method. I'll let you know if I get it. BTW, TPT is "to prove that".
- #6
Aditya89
- 23
- 0
Hey does anybody know how to create mathematical symbols while posting?
- #7
matt grime
Science Advisor
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THnigs like ab=k^2, k \in \mathbb{N}?
Try looking up the LaTeX sticky post in the physics section. Or trying seraching the site using the search function for such "frequently asked questions"
Try looking up the LaTeX sticky post in the physics section. Or trying seraching the site using the search function for such "frequently asked questions"
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