Solving for Integers a and b in a Divisibility Equation

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Discussion Overview

The discussion revolves around finding integers a and b in a divisibility equation, specifically whether there exists an integer n such that a divides b^n. The scope includes mathematical reasoning and exploration of divisibility criteria based on prime factorization.

Discussion Character

  • Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant presents the integers a and b along with their prime factorizations, posing the question of whether an integer n exists such that a divides b^n.
  • Another participant questions the criteria necessary for one positive integer to divide another, suggesting that prime factorizations may be relevant.
  • A third participant expresses confusion regarding the previous explanation and suggests that dividing the factorizations might lead to the answer.
  • A fourth participant questions the necessity of the thread and proposes simpler related questions about divisibility involving powers of 2 and their conditions.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as there are differing levels of understanding and approaches to the problem, with some participants suggesting simpler related questions while others focus on the original divisibility question.

Contextual Notes

Limitations include potential missing assumptions regarding the conditions under which divisibility holds and the specific values of n that satisfy the original question.

clueles
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a = 238000 = 2^4 x 5^3 x 7 x 17 and b = 299880 = 2^3 x 3^2 x 5 x 7^2 x 17

is there an integer n so that a divides b^n if so what is the smallest possibility for n
 
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What criterion are needed for one positive integer to divide another, if both of them are greater than 1 (Hint: Might prime factorizations have something to do with it?)?
 
i'm sorry i really don't follow your explanation. my guess that you have to divide the factorizations and that could possibly give you the answer
 
Was another thread on the same topic necessary?

Here's a simpler question, for what values of k does 2^4 divide 2^k?

For what values of k and l does (2^4)x(5^3) divide (2^k)x(5^l)?

If you can answer these, you should be able to handle your question.
 

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