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Contests
National and Regional Contests
Moldova Contests
Moldova Team Selection Test
2019 Moldova Team Selection Test
12
12
Part of
2019 Moldova Team Selection Test
Problems
(1)
number theory problem
Source: Moldova TST 2019
3/10/2019
Let
p
≥
5
p\ge 5
p
≥
5
be a prime number. Prove that there exist positive integers
m
m
m
and
n
n
n
with
m
+
n
≤
p
+
1
2
m+n\le \frac{p+1}{2}
m
+
n
≤
2
p
+
1
for which
p
p
p
divides
2
n
⋅
3
m
−
1.
2^n\cdot 3^m-1.
2
n
⋅
3
m
−
1.
number theory
prime numbers