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Putnam
2015 Putnam
B3
B3
Part of
2015 Putnam
Problems
(1)
Putnam 2015 B3
Source:
12/6/2015
Let
S
S
S
be the set of all
2
×
2
2\times 2
2
×
2
real matrices
M
=
(
a
b
c
d
)
M=\begin{pmatrix}a&b\\c&d\end{pmatrix}
M
=
(
a
c
b
d
)
whose entries
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
(in that order) form an arithmetic progression. Find all matrices
M
M
M
in
S
S
S
for which there is some integer
k
>
1
k>1
k
>
1
such that
M
k
M^k
M
k
is also in
S
.
S.
S
.
Putnam
Putnam 2015
Putnam matrices