Difference between revisions of "1986 AIME Problems/Problem 5"
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[[Category:Intermediate Number Theory Problems]] | [[Category:Intermediate Number Theory Problems]] | ||
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Revision as of 19:04, 4 July 2013
Problem
What is that largest positive integer for which
is divisible by
?
Solution
If ,
. Using the Euclidean algorithm, we have
, so
must divide 900. The greatest integer
for which
divides 900 is 890; we can double-check manually and we find that indeed
.
In a similar manner, we can apply synthetic division. We are looking for . Again,
must be a factor of
.
See also
1986 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
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