# Enumerating integers n s.t. 36 | 48n

• I
• Mr Davis 97
In summary, the task is to find a list of numbers for n where 36 divides 48*n in the fastest way possible. This can be achieved by determining what values n should be so that the product of 48*n contains the factors of 36, specifically 2*2*3*3. An alternative approach would be to first create a list of numbers where n is true and then deducing the fastest algorithm from there.

#### Mr Davis 97

This is a simple computational question. Let ##n \in [0, 36)##. What's the fastest way to list all ##n## s.t ##36## divides ##48n##?

Well first I would get a list of numbers for n where it is true and from there deduce the fastest algorithm to list them.

Alternatively, you can look at what n should be such that 48*n contains the factors of 36 namely 2*2*3*3.

so what must n provide so that the product contains the factors of 36?

Mr Davis 97 said:
Let n∈[0,36)
This notation is a bit odd, as it implies that n belongs to the real interval. A better way to write it IMO would be
##\text{Let } n \in \{0, 1, 2, \dots, 35\}##

jedishrfu said:
Alternatively, you can look at what n should be such that 48*n contains the factors of 36 namely 2*2*3*3.
I would probably do this first, rather than as an alternate approach.

jedishrfu

## What does it mean to "enumerate integers n s.t. 36 | 48n"?

To enumerate integers n s.t. 36 | 48n means to list out all possible values of n that satisfy the condition that 36 is a multiple of 48n. In other words, 36 is evenly divisible by 48n without any remainder.

## What is the significance of the number 36 in this question?

The number 36 is significant because it is the constant, or divisor, in the given condition. In order for 36 to be a multiple of 48n, n must be a factor of 36.

## Can you provide examples of integers n that satisfy the condition 36 | 48n?

Some examples of integers n that satisfy the condition 36 | 48n are 1, 2, 3, 4, 6, 9, 12, 18, and 36. These are all factors of 36, and when multiplied by 48, result in a multiple of 36.

## Are there any restrictions on the values of n that can satisfy the condition 36 | 48n?

Yes, there are restrictions. In order for 36 | 48n to be true, n must be a positive integer. It cannot be a negative number or a fraction. Additionally, n cannot be 0 since any number multiplied by 0 is 0, which would not satisfy the condition.

## How many integers n satisfy the condition 36 | 48n?

There are infinitely many integers n that satisfy the condition 36 | 48n. This is because there are an infinite number of factors of 36, and each of these factors can be multiplied by 48 to result in a multiple of 36. Therefore, the list of integers n will continue indefinitely.