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IMO Shortlist 2010 - Problem N2
IMO Shortlist 2010 - Problem N2
Source:
July 17, 2011
modular arithmetic
number theory
equation
IMO Shortlist
LTE Lemma
Problem Statement
Find all pairs
(
m
,
n
)
(m,n)
(
m
,
n
)
of nonnegative integers for which
m
2
+
2
⋅
3
n
=
m
(
2
n
+
1
−
1
)
.
m^2 + 2 \cdot 3^n = m\left(2^{n+1} - 1\right).
m
2
+
2
⋅
3
n
=
m
(
2
n
+
1
−
1
)
.
Proposed by Angelo Di Pasquale, Australia
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