2024 USAJMO Problems/Problem 3
Contents
Problem
Let be the sequence defined by
and
for each integer
. Suppose that
is prime and
is a positive integer. Prove that some term of the sequence
is divisible by
.
Solution 1
Lemma :
Given a prime , a positive integer
, and an even
such that
, we must have that
.
Proof of Lemma :
Therefore,
See Also
2024 USAJMO (Problems • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
1 • 2 • 3 • 4 • 5 • 6 | ||
All USAJMO Problems and Solutions |
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