Difference between revisions of "Mock AIME 3 Pre 2005 Problems/Problem 8"
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− | + | ==Problem== | |
+ | Let <math>N</math> denote the number of <math>8</math>-tuples <math>(a_1, a_2, \dots, a_8)</math> of real numbers such that <math>a_1 = 10</math> and | ||
<math>\left|a_1^{2} - a_2^{2}\right| = 10</math> | <math>\left|a_1^{2} - a_2^{2}\right| = 10</math> | ||
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Determine the remainder obtained when <math>N</math> is divided by <math>1000</math>. | Determine the remainder obtained when <math>N</math> is divided by <math>1000</math>. | ||
+ | |||
+ | ==Solution== | ||
+ | {{solution}} | ||
+ | |||
+ | ==See also== |
Revision as of 07:32, 14 February 2008
Problem
Let denote the number of -tuples of real numbers such that and
Determine the remainder obtained when is divided by .
Solution
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