Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

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

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

Offline

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

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)*

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

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.

**228** books currently added on Goodreads

Offline