Can a Number Have Over 2017 Divisors Within a Specific Range?

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In summary, the user is requesting help with a task involving proving the existence of a number with more than 2017 divisors that satisfy a given inequality. The user has been reminded to show their progress or thoughts on the task before receiving help.
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anre
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Hello
could you help me to solve my task

$n \in \Bbb{N}$
Prove that there is n which has more than 2017 divisors d that:

$\sqrt{n} \le d < 1,01 * \sqrt{n}$

Thank you
 
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Hello anre and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 

FAQ: Can a Number Have Over 2017 Divisors Within a Specific Range?

What are divisors of a natural number n?

Divisors of a natural number n are all the numbers that can divide n without leaving a remainder. In other words, they are the factors of n.

How can I find the divisors of a natural number n?

To find the divisors of a natural number n, you can simply list all the numbers that divide n without leaving a remainder. Alternatively, you can use a mathematical formula such as the prime factorization method or the trial division method.

What is the relationship between divisors of a natural number n and its prime factors?

The divisors of a natural number n are the products of its prime factors. In other words, the divisors of n are the combinations of its prime factors.

What is the total number of divisors of a natural number n?

The total number of divisors of a natural number n is equal to the number of combinations of its prime factors plus one. For example, if n=12, its prime factors are 2, 2, and 3. Therefore, the total number of divisors is (2+1)(2+1)=9.

What is the relationship between the number of divisors of a natural number n and its prime factorization?

The number of divisors of a natural number n is equal to the product of adding one to each exponent in its prime factorization. For example, if n=12, its prime factorization is 2^2 x 3^1. Therefore, the number of divisors is (2+1)(1+1)=6.

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