I tried with comparing highest exponents

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In summary, the conversation discusses how to prove that (2^m - 1) and (2^n - 1) are not the only prime factors of z, where z = (2^(mn) - 1)/[(2^m - 1)(2^n - 1)] and (2^m - 1) and (2^n - 1) are prime numbers. The speaker mentions trying to solve it by writing z as (2^m - 1)^a * (2^n - 1)^b and proving it is not correct, but is unsure of how to do so. They also suggest proving that 2^(mn) - 1 cannot be written as ((2^m -
  • #1
helgamauer
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We have:
z = (2^(mn) - 1)/[(2^m - 1)(2^n - 1)], where (2^m - 1) and (2^n - 1) are prime numbers.
Prove that (2^m - 1) and (2^n - 1) are not the only prime factors of z.

I tried to solve it writing z = (2^m - 1)^a * (2^n - 1)^b and proving that it is not correct. But I don't know how. I also noticed that it would be sufficient to prove that 2^(mn) - 1 can't be written as ((2^m - 1)^x * (2^n - 1)^y but I also have no idea how to prove it. I tried with comparing highest exponents, but nothing..
It will be fantastic if you help me with proving this fact.
 
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  • #2


* And i meant (2^m -1) and (2^n -1) are two different ODD primes. May anybody help?
 

1. What does it mean to compare highest exponents?

Comparing highest exponents means to compare the highest powers or degrees of a variable in a polynomial equation. This can help determine which term has the greatest influence on the overall value of the equation.

2. How do you compare highest exponents?

To compare highest exponents, you would first identify the variable with the highest exponent in each term of the polynomial equation. Then, you can compare the exponents to see which one is the largest. If the exponents are the same, you would compare the coefficients, or the numbers in front of the variables.

3. Why is it important to compare highest exponents?

Comparing highest exponents can help us understand the behavior and characteristics of a polynomial equation. It can also help us solve equations and identify the most significant terms in a polynomial expression.

4. Can you compare highest exponents in different variables?

Yes, you can compare highest exponents in different variables. However, it is important to note that you cannot directly compare exponents in different variables. Instead, you would need to rewrite the equation in terms of the same variable and then compare the exponents.

5. How does comparing highest exponents relate to polynomial degree?

Comparing highest exponents is closely related to polynomial degree, as the degree of a polynomial is determined by the highest exponent of the variable in the equation. Therefore, by comparing highest exponents, we can also determine the degree of a polynomial.

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