Solving for Integers a and b in a Divisibility Equation

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In summary, the conversation discussed the prime factorizations of two numbers, a and b, and the possibility of one number dividing another. The criteria for this were related to the prime factorizations and determining the smallest possible value for n. The conversation also mentioned a simpler question regarding the values of k in relation to 2^4, and then expanded to include values of k and l for (2^4)x(5^3) and (2^k)x(5^l). The speaker suggested that understanding these questions would assist in answering the original question.
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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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  • #2
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?)?
 
  • #3
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
 
  • #4
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.
 

Related to Solving for Integers a and b in a Divisibility Equation

1. What are integers?

Integers are whole numbers that do not have any fractional or decimal parts. They can be positive, negative, or zero.

2. How do you find integers on a number line?

To find integers on a number line, start at zero and move either to the left or right. The numbers you encounter will be integers. Positive integers are to the right of zero and negative integers are to the left.

3. How do you determine if a number is an integer?

A number is an integer if it has no decimal or fractional parts. This means that it is a whole number. For example, 5 is an integer while 5.5 is not.

4. What are the rules for adding and subtracting integers?

When adding integers with the same sign, you add their absolute values and keep the sign. When adding integers with different signs, subtract the smaller absolute value from the larger one and keep the sign of the larger number. When subtracting integers, add the opposite of the second number to the first number.

5. How are integers used in real life?

Integers are used in many real-life situations, such as keeping track of money, counting objects, and measuring temperature. They are also used in mathematical equations and algorithms to solve problems and make predictions.

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