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Putnam
1992 Putnam
A3
Beautiful Problem
Beautiful Problem
Source:
July 16, 2016
number theory
Problem Statement
Let
m
,
n
m,n
m
,
n
are natural numbers such that
G
C
D
(
m
,
n
)
=
1
GCD(m,n)=1
GC
D
(
m
,
n
)
=
1
.Find all triplets
(
x
,
y
,
n
)
(x,y,n)
(
x
,
y
,
n
)
which sastify
(
x
2
+
y
2
)
m
=
(
x
y
)
n
(x^2+y^2)^m=(xy)^n
(
x
2
+
y
2
)
m
=
(
x
y
)
n
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