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## #1 2013-11-15 13:04:30

cooljackiec
Member
Registered: 2012-12-13
Posts: 185

### solutions

There are exactly four positive integers such that

is an integer. Compute the largest such n

i only found negative solutions

I see you have graph paper.
You must be plotting something

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## #2 2013-11-15 13:49:00

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: solutions

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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## #3 2013-11-15 19:54:30

Nehushtan
Member
Registered: 2013-03-09
Posts: 897
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### Re: solutions

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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