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National and Regional Contests
China Contests
China Team Selection Test
2006 China Team Selection Test
2
Find (a,n)
Find (a,n)
Source: China TST 2006 (1)
March 24, 2006
number theory
China TST
Hi
Problem Statement
Find all positive integer pairs
(
a
,
n
)
(a,n)
(
a
,
n
)
such that
(
a
+
1
)
n
−
a
n
n
\frac{(a+1)^n-a^n}{n}
n
(
a
+
1
)
n
−
a
n
is an integer.
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