Find all integers n for which this fraction is an integer

In summary, a fraction is considered an integer when the numerator is divisible by the denominator without any remainder. To determine if a fraction is an integer, you can divide the numerator by the denominator and check if the result is a whole number. Not all fractions can be integers, only those where the numerator is divisible by the denominator without any remainder. There are some rules and patterns that can help identify integers in fractions, such as having a denominator of 1 or having a common factor in both the numerator and denominator. To find all integers n for which a given fraction is an integer, you can use algebraic manipulation to solve for n.
  • #1
mr.green717
2
0
Find all integers n for which the fraction n ^ 3 + 2010 / (n ^ 2 + 2010) is equal to integer.

please I need help :( Thank you
 
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  • #2


Which values immediately come to your mind?
 
  • #3


0 and 1
 
  • #4


Right, those are the only two that are easy to find. Another possibility would have been to find an integer such that n^3 + 2010=0 but there are none. If you have any programming skill you could try and brute force it with a relatively easy to implement algorithm.
 

Related to Find all integers n for which this fraction is an integer

1. What does it mean for a fraction to be an integer?

A fraction is an integer when the numerator (top number) is divisible by the denominator (bottom number) without any remainder. This means that the result of the division is a whole number, without any decimals or fractions.

2. How do you determine if a fraction is an integer?

To determine if a fraction is an integer, you can divide the numerator by the denominator. If the result is a whole number, then the fraction is an integer.

3. Can any fraction be an integer?

No, not all fractions can be integers. Only fractions where the numerator is divisible by the denominator without any remainder can be an integer.

4. Are there any specific rules or patterns for finding integers in fractions?

Yes, there are some rules and patterns that can help identify integers in fractions. For instance, if the fraction has a denominator of 1, then the numerator is the integer. Also, if the fraction has a common factor in both the numerator and denominator, it can be simplified to an integer.

5. How do you find all integers n for which a given fraction is an integer?

To find all integers n for which a fraction is an integer, you can use algebraic manipulation. Take the given fraction and set it equal to n, then solve for n using algebraic operations. The resulting values of n will be all the possible integers for which the fraction is also an integer.

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