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All-Russian Olympiad Regional Round
2005 All-Russian Olympiad Regional Round
10.7
10.7
Part of
2005 All-Russian Olympiad Regional Round
Problems
(1)
Slightly modified Fermat equation has many solutions
Source: All-Russian MO Round 4, 2005
4/2/2005
10.7 Find all pairs
(
a
,
b
)
(a,b)
(
a
,
b
)
of natural numbers s.t.
a
n
+
b
n
a^n+b^n
a
n
+
b
n
is a perfect
n
+
1
n+1
n
+
1
th power for all
n
ā
N
n\in\mathbb{N}
n
ā
N
. (V. Senderov)
number theory proposed
number theory