2003 JBMO Problems/Problem 1
Revision as of 23:14, 27 August 2018 by Rockmanex3 (talk | contribs) (Solution to Problem 1 -- kinda like 1998 JBMO Problem 1)
Problem
Let be a positive integer. A number consists of digits, each of which is 4; and a number consists of digits, each of which is 8. Prove that is a perfect square.
Solution
Using the definition of base 10, we know that Thus, we have Since we know that is an integer, we confirm that is a perfect square.
See Also
2003 JBMO (Problems • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
1 • 2 • 3 • 4 | ||
All JBMO Problems and Solutions |