Difference between revisions of "1984 IMO Problems/Problem 2"
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This solution was posted and copyrighted by ZetaX. The original thread for this problem can be found here: [https://aops.com/community/p366644] | This solution was posted and copyrighted by ZetaX. The original thread for this problem can be found here: [https://aops.com/community/p366644] | ||
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== See Also == {{IMO box|year=1984|num-b=1|num-a=3}} | == See Also == {{IMO box|year=1984|num-b=1|num-a=3}} |
Latest revision as of 11:30, 26 June 2024
Problem
Find one pair of positive integers such that
is not divisible by
, but
is divisible by
.
Solution 1
So we want and
, so we want
.
Now take e.g.
and get
. Now by some standard methods like Hensels Lemma (used to the polynomial
, so
seen as constant from now) we get also some
with
and
, so
and we are done. (in this case it gives
)
This solution was posted and copyrighted by ZetaX. The original thread for this problem can be found here: [1]
See Also
1984 IMO (Problems) • Resources | ||
Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
All IMO Problems and Solutions |