1986 AIME Problems/Problem 5
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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 substitution. We are looking for 
. Again, must be a factor of 
.
See also
| 1986 AIME (Problems • Resources) | ||
| Preceded by Problem 4 | Followed by Problem 6 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
