# Simple proof check

1. Aug 9, 2009

### Fisicks

Recently I've stumbled upon number theory and decided to order a book which is coming soon so in the mean time I've decided to try what looked like an easy proof to kinda practice on. So tell me where my logic fails or where it surprisingly doesn't. criticism appreciated.

http://img210.imageshack.us/img210/3406/img054i.jpg" [Broken]

Last edited by a moderator: May 4, 2017
2. Aug 10, 2009

### CRGreathouse

The "investigate" line doesn't justify why
n^2/6 = 6k^2
which is the crux of the proof.

3. Aug 10, 2009

### Fisicks

well i just found a pattern, and it holds.

ex. the 15th natural number squared divisible by 6 is 8100. So K is 15, and you have
8100/6=6*15^2
1350=1350

4. Aug 11, 2009

### Fisicks

Can someone give me more insight on what greathouse said, and how to salvage this proof? Its not like n^2/6=6k^2 isn't true for my conditions.

5. Aug 11, 2009

### ramsey2879

try every integer has a unique prime factorization and represent a number divisible by 6 as a product of its prime factors. explain why square numbers have only even exponents in their prime factorization. Use these to justify your logic.