MathDB
Problems
Contests
National and Regional Contests
Germany Contests
German National Olympiad
2016 German National Olympiad
4
4
Part of
2016 German National Olympiad
Problems
(1)
Integer equation with Binomial Coefficients
Source:
6/21/2016
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)
binomial coefficients