Find a: Solve Discrete Math Problem with a & x Intergers

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    Discrete Discrete math
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Discussion Overview

The discussion revolves around solving a discrete mathematics problem involving integer variables a and x, where a must divide two linear expressions involving x. Participants seek to find the value of a given the conditions specified.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents the problem and expresses uncertainty about how to begin solving it.
  • Another participant suggests expressing the equations in terms of integers p and q to facilitate elimination of x.
  • A different participant, unfamiliar with number theory, proposes a method to manipulate the equations to derive a relationship involving a, leading to the conclusion that a must divide 37.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the solution, and there are varying levels of familiarity with the underlying concepts, leading to different approaches being suggested.

Contextual Notes

Some participants express uncertainty about the steps involved in eliminating x and the implications of the derived relationships. The discussion includes assumptions about the nature of a and x being positive integers.

boiseneon
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ok the problem is

Given that a and x are intergers, a>1, a|(11x+3), a|(55x+52), find a.

I am not sure how to even start this one to find a...any help please :cry:
 
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There are integers p, q such that

11x + 3 = pa,
55x + 52 = qa.

Try eliminating x...
 
ok how do I eliminate x??
 
I am not at all familiar with number theory but I think got the answer:
First of all we have a>1>0 and x>0

11x+3=pa<=>55x+15=5pa (1)
55x+52=qa (2)

(2)-(1)=>37=(q-5p)a
q,p are natural numbers
So a|37 and 37 is a prime=> ...
 

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