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German National Olympiad
2016 German National Olympiad
4
Integer equation with Binomial Coefficients
Integer equation with Binomial Coefficients
Source:
June 21, 2016
binomial coefficients
Problem Statement
Find all positive integers
m
,
n
m,n
m
,
n
with
m
≤
2
n
m \leq 2n
m
≤
2
n
that solve the equation
m
⋅
(
2
n
n
)
=
(
m
2
2
)
.
m \cdot \binom{2n}{n} = \binom{m^2}{2}.
m
⋅
(
n
2
n
)
=
(
2
m
2
)
.
(German MO 2016 - Problem 4)
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