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2023 HMIC
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2023 HMIC
Problems
(1)
Mundane Primes
Source: 2023 HMIC P2
4/25/2023
A prime number
p
p
p
is mundane if there exist positive integers
a
a
a
and
b
b
b
less than
p
2
\tfrac{p}{2}
2
p
such that
a
b
−
1
p
\tfrac{ab-1}{p}
p
ab
−
1
is a positive integer. Find, with proof, all prime numbers that are not mundane.
HMIC