All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
Never a square (Posted on 2017-02-26) Difficulty: 4 of 5
Let each of x1, x2, x3, …, x777, y1, y2, y3, …, y777 be an arbitrary non-zero integer number.
Consider the product

P = (2x12 +3y12) * (2x22 +3y22) * (2x32 +3y32) * ...* (2x7772 +3y7772).

Prove: P cannot be a square number.

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts Poossible solution | Comment 1 of 5

Let the sequence  x^2 + 6y^2 {1, 4, 6, 7, 9, 10, 15, 16,..} be 'Chalk'; let the sequence 2x^2 + 3y^2 {0, 2, 3, 5, 8, 11, 12, 14, 18, 20...)be 'Cheese'.

Cheese*Cheese = Chalk; e.g. = 2*2 = 4, 5*2=10.

Cheese*Chalk = Cheese; e.g.2*4=8,4*3=12,2*10=20.

The sequence 'Chalk' contains every square; the sequence 'Cheese' contains none.

Hence P cannot be square.


  Posted by broll on 2017-02-27 01:21:33
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 (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information