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Eotvos Mathematical Competition (Hungary)
1932 Eotvos Mathematical Competition
1
1
Part of
1932 Eotvos Mathematical Competition
Problems
(1)
(a+1)^b-1 is divisible by a^{n+1} when b is divisible by a^n
Source: Eotvos 1932 p1
9/10/2024
Let
a
,
b
a, b
a
,
b
and
n
n
n
be positive integers such that
b
b
b
is divisible by
a
n
a^n
a
n
. Prove that
(
a
+
1
)
b
ā
1
(a+1)^b-1
(
a
+
1
)
b
ā
1
is divisible by
a
n
+
1
a^{n+1}
a
n
+
1
.
number theory
divisible