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**cooljackiec****Member**- Registered: 2012-12-13
- Posts: 160

There are exactly four positive integers such that

is an integer. Compute the largest such ni only found negative solutions

I see you have graph paper.

You must be plotting something

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

For that to be an integer, 484 must be divisible by (n+23).

The positive solutions are 21, 98, 219, 461.

*Last edited by anonimnystefy (2013-11-15 13:53:17)*

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This is an integer if and only if 484 is divisible by *n*+23. The factors of 484 are ±1, ±2, ±4, ±11, ±22, ±44, ±121, ±242, ±484 so there are 18 solutions altogether. The positive ones are given by *n* + 23 = 44, 121, 242, 484.

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