Difference between revisions of "2002 AMC 12P Problems/Problem 13"
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== Problem == | == Problem == | ||
| − | + | What is the maximum value of <math>n</math> for which there is a set of distinct positive integers <math>k_1, k_2, ... k_n</math> for which | |
| − | <math> \ | + | <cmath>k^2_1 + k^2_2 + ... + k^2_n = 2002?</cmath> |
| + | |||
| + | <math> | ||
| + | \text{(A) }14 | ||
| + | \qquad | ||
| + | \text{(B) }15 | ||
| + | \qquad | ||
| + | \text{(C) }16 | ||
| + | \qquad | ||
| + | \text{(D) }17 | ||
| + | \qquad | ||
| + | \text{(E) }18 | ||
| + | </math> | ||
== Solution == | == Solution == | ||
Revision as of 23:50, 29 December 2023
Problem
What is the maximum value of 
for which there is a set of distinct positive integers 
for which
![\[k^2_1 + k^2_2 + ... + k^2_n = 2002?\]](http://latex.artofproblemsolving.com/7/d/a/7da913f9b8644e18078f96cf0ab0c4e928633633.png)
Solution
If 
, then 
. Since 
, 
must be 
to some factor of 6. Thus, there are four (3, 9, 27, 729) possible values of 
.
See also
| 2002 AMC 12P (Problems • Answer Key • Resources) | |
| Preceded by Problem 12 |
Followed by Problem 14 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
