Find all integers n for which this fraction is an integer

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Homework Help Overview

The problem involves finding all integers n for which the fraction (n^3 + 2010) / (n^2 + 2010) is an integer. The subject area pertains to number theory and algebraic expressions.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss potential integer values for n, with some suggesting simple integers like 0 and 1. There is also mention of exploring the condition where n^3 + 2010 equals zero, although it is noted that no integers satisfy this.

Discussion Status

The discussion is ongoing, with participants sharing initial thoughts and exploring various integer candidates. Some guidance has been offered regarding programming approaches to find solutions, indicating a productive direction without reaching a consensus.

Contextual Notes

Participants are operating under the constraint of finding integer solutions and are considering the implications of the fraction being an integer.

mr.green717
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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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Which values immediately come to your mind?
 


0 and 1
 


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.
 

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