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All-Russian Olympiad Regional Round
2005 All-Russian Olympiad Regional Round
8.7
x + y = a^n, x^2 + y^2 = a^m All-Russian MO 2005 Regional (R4) 8.7
x + y = a^n, x^2 + y^2 = a^m All-Russian MO 2005 Regional (R4) 8.7
Source:
August 26, 2024
number theory
diophantine
system of equations
Problem Statement
Find all pairs
(
x
,
y
)
(x, y)
(
x
,
y
)
of natural numbers such that
x
+
y
=
a
n
,
x
2
+
y
2
=
a
m
x + y = a^n, x^2 + y^2 = a^m
x
+
y
=
a
n
,
x
2
+
y
2
=
a
m
for some natural
a
,
n
,
m
a, n, m
a
,
n
,
m
.
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