1997 AIME Problems/Problem 1
Problem
How many of the integers between 1 and 1000, inclusive, can be expressed as the difference of the squares of two nonnegative integers?
Solution
Notice that all odd numbers can be obtained by using 
where 
is a nonnegative integer. All multiples of 
can be obtained by using 
, where 
is a positive integer. Numbers congruent to 
cannot be obtained because squares are 
Thus, the answer is 
See also
| 1997 AIME (Problems • Answer Key • Resources) | ||
| Preceded by First Question |
Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
