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

Home > Just Math
Find the sum (Posted on 2016-02-29) Difficulty: 2 of 5
The difference between two positive integers is 56.
If their squares have both the same units digit and the same tens digit, find the sum of the two positive integers.

1. Find the minimal couple, complying with the above, and the corresponding sum.
2. Define formulas for additional solutions (both numbers and their sums).

See The Solution Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution | Comment 1 of 2

The pair {78,22} have a difference of 56, while their squares are 6084 and 484. 78+22=100. Obviously, if squares have the same two terminal digits, their difference will be divisible by 100.

a=(78+25k), b=(22+25k) gives a^2-b^2=2800(k+2). The sum in each case is 50(k+2), for all k.

Edited on February 29, 2016, 8:27 am
  Posted by broll on 2016-02-29 08:25:26

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