Possible Triplets for (1+1/a)(1+1/b)(1+1/c)=3

  • Context: Undergrad 
  • Thread starter Thread starter rattanjot
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Discussion Overview

The discussion revolves around finding integer triplets \( (a, b, c) \) that satisfy the equation \( (1 + \frac{1}{a})(1 + \frac{1}{b})(1 + \frac{1}{c}) = 3 \). The scope includes mathematical reasoning and problem-solving techniques.

Discussion Character

  • Exploratory, Mathematical reasoning, Homework-related

Main Points Raised

  • One participant suggests multiplying out the expression to explore the equation further.
  • Another participant proposes considering the condition \( a \geq b \geq c \) and inquires about the maximum value of \( c \).
  • A different participant mentions that the problem resembles a standard max/min problem and suggests the use of Lagrange multipliers as a potential method for solving it.
  • There is a request for clarification on what Lagrange multipliers are.
  • One participant asks for more context about the problem to provide better suggestions.

Areas of Agreement / Disagreement

Participants have not reached a consensus, and multiple approaches and viewpoints are presented without resolution.

Contextual Notes

The discussion does not clarify the assumptions regarding the values of \( a, b, \) and \( c \) or the specific methods that participants have attempted so far.

rattanjot
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let a,b,c be integers
how many triplets are possible for
(1+1/a)(1+1/b)(1+1/c) = 3
 
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Why don't you multiply it out and see what happens?
 
Consider that a≥b≥c. can u please tell the maximum value of c..!
 
What have you tried so far? Yours seems like a standard max/min problem that can be done, e.g., by Lagrange multipliers.
 
What are Langrange multipliers..??
 
Maybe if you tell us more about the context of the problem and the areas that you

know, we can have a better way of suggesting something useful.
 

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