Difference between revisions of "AoPS Wiki:Problem of the Day/September 6, 2011"
(Created page with "The integers <math>a,b,c,d</math> satisfy <math>a > b > c > d</math> and \[ a + b + c + d = 2048 \ \textrm{ and }\ a^2 - b^2 + c^2 - d^2 = 2048. \] Find the smallest possible val...") |
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The integers <math>a,b,c,d</math> satisfy <math>a > b > c > d</math> and | The integers <math>a,b,c,d</math> satisfy <math>a > b > c > d</math> and | ||
| − | + | <cmath> | |
a + b + c + d = 2048 \ \textrm{ and }\ a^2 - b^2 + c^2 - d^2 = 2048. | a + b + c + d = 2048 \ \textrm{ and }\ a^2 - b^2 + c^2 - d^2 = 2048. | ||
| − | + | </cmath> | |
Find the smallest possible value of <math>a</math>. | Find the smallest possible value of <math>a</math>. | ||
Revision as of 17:25, 6 September 2011
The integers 
satisfy 
and
![\[a + b + c + d = 2048 \ \textrm{ and }\ a^2 - b^2 + c^2 - d^2 = 2048.\]](http://latex.artofproblemsolving.com/0/f/c/0fc80cc458ea97a1248d30fc5778b0b6d9ff739c.png)
Find the smallest possible value of 
.
