Not an official ACM page
[Problem D | 1993 East-Central Regional problem set | My ACM problem archive | my home page]

1993 East-Central Regionals of the ACM International Collegiate Programming Contest

Problem C

Count on Cantor

One of the famous proofs of modern mathematics is Georg Cantor's demonstration that the set of rational numbers is enumerable. The proof works by using an explicit enumeration of rational numbers as shown in the diagram below. 
1/1 1/2 1/3 1/4 1/5 ...
2/1 2/2 2/3 2/4
3/1 3/2 3/3
4/1 4/2
5/1
In the above diagram, the first term is 1/1, the second term is 1/2, the third term is 2/1, the fourth term is 3/1, the fifth term is 2/2, and so on.

You are to write a program that will read a list of numbers in the range from 1 to 10 7 and will print for each number the corresponding term in Cantor's enumeration as given below. No blank line should appear after the last number. The input list contains a single number per line and will be terminated by end-of-file. No more than 30 numbers will appear in the input file.

Sample Input

3
14
7

Sample Output

TERM 3 IS 2/1
TERM 14 IS 2/4
TERM 7 IS 1/4
This page maintained by Ed Karrels.
Last updated November 6, 1997