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## #1 2013-11-16 12:04:30

cooljackiec
Full Member

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### 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

## #2 2013-11-16 12:49:00

anonimnystefy
Real Member

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### 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 (2013-11-16 12:53:17)

The limit operator is just an excuse for doing something you know you can't.
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“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #3 2013-11-16 18:54:30

Nehushtan
Power Member

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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.