## Welcome to BrainDen.com - Brain Teasers Forum

 Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account. As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends. Of course, you can also enjoy our collection of amazing optical illusions and cool math games. If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top. If you have a website, we would appreciate a little link to BrainDen. Thanks and enjoy the Den :-)
Guest Message by DevFuse

# Powers separated by 5

14 replies to this topic

Senior Member

• Members
• 1837 posts
• Gender:Female

Posted 08 April 2013 - 11:23 PM

Find pairs of positive integers where 2a = 3b + 5.  Prove that you have found them all.

• 0

### #2 bonanova

bonanova

bonanova

• Moderator
• 6161 posts
• Gender:Male
• Location:New York

Posted 09 April 2013 - 11:23 AM

Spoiler for for starters

• -1

Vidi vici veni.

Senior Member

• Members
• 1837 posts
• Gender:Female

Posted 09 April 2013 - 02:10 PM

Bonanova,

Do you mean 2^2 = 3^2 + 5 ?
• 0

### #4 TimeSpaceLightForce

TimeSpaceLightForce

Senior Member

• Members
• 705 posts
• Gender:Male

Posted 09 April 2013 - 03:03 PM

Spoiler for 2

• 0

Senior Member

• Members
• 1837 posts
• Gender:Female

Posted 09 April 2013 - 06:11 PM

This is a good start.

Spoiler for 2

• 0

### #6 bonanova

bonanova

bonanova

• Moderator
• 6161 posts
• Gender:Male
• Location:New York

Posted 09 April 2013 - 07:50 PM

Bonanova,
Do you mean 2^2 = 3^2 + 5 ?

I plead drowsiness. I read the puzzle incorrectly. Minus 5 obviously.
• 0

Vidi vici veni.

Senior Member

• Members
• 1837 posts
• Gender:Female

Posted 05 May 2013 - 01:51 AM

Spoiler for hint, to get you started

• 0

### #8 TimeSpaceLightForce

TimeSpaceLightForce

Senior Member

• Members
• 705 posts
• Gender:Male

Posted 09 May 2013 - 05:34 PM

I cant find the those elusive evens ..using excel i formulate the 2 expressions with 1-300 exponents ,

add both on a column , sort ascending and check for equal consecutive..

• 0

Senior Member

• Members
• 1837 posts
• Gender:Female

Posted 09 May 2013 - 09:16 PM

Spoiler for hint 2

• 0

Senior Member

• Members
• 1837 posts
• Gender:Female

Posted 11 May 2013 - 07:06 PM

Spoiler for hint 3

• 0

#### 0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users