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

Home > Just Math
sod(square) - number = 2 (Posted on 2010-09-27) Difficulty: 3 of 5
(I) Determine all possible values of a base-10 positive integer x such that:
sod(x2) - x = 2, where sod(n) denotes the sum of the digits in the base-10 representation of n.

(II) Determine all possible values of a base-11 positive integer y such that:
sod(y2) - y = 2, where sod(n) denotes the sum of the digits in the base-11 representation of n.

In each of (I) and (II) prove that these are the only respective valid value(s) corresponding to x and y.

No Solution Yet Submitted by K Sengupta    
Rating: 2.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts Some numbers satisfying Part (1) | Comment 1 of 2

By observation i found that 2, 5, 8, 14, 17 satisfy the first part.

Higher values dont as the sum of digits increases by only a few and number increases by a lot. Cant prove it though.

EDIT: 2, 4, 7, 9 will satisfy part 2.

Edited on September 27, 2010, 4:07 pm
  Posted by Vishal Gupta on 2010-09-27 16:04:13

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 (8)
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