All about
flooble

fun stuff

Get a free chatterbox

Free JavaScript

Avatars
perplexus
dot
info
Home
>
Just Math
Changing form (
Posted on 20130629
)
Define a product a*b with a and b not necessarily distinct integers in {2,3,4,...}.
Show that a*b is always expressible as xy + xz + yz + 1, with x, y, and z positive integers.
Source: rephrased Putnam competition.
No Solution Yet
Submitted by
Ady TZIDON
No Rating
Comments: (
Back to comment list
 You must be logged in to post comments.
)
Transformation (spoiler)
Comment 1 of 1
Let x = a1
y = b1
z = 1
Then ab = (x+1)(y+1)
= xy + x + y + 1
= xy + xz + yz + 1
q.e.d
Posted by
Steve Herman
on 20130629 20:33:30
Please log in:
Login:
Password:
Remember me:
Sign up!

Forgot password
Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ

About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On
Chatterbox:
blackjack
flooble's webmaster puzzle
Copyright © 2002  2019 by
Animus Pactum Consulting
. All rights reserved.
Privacy Information