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Baltic Way
1995 Baltic Way
2
a^2+k divides (a-1)a(a+1)
a^2+k divides (a-1)a(a+1)
Source: Baltic Way 1995
October 8, 2011
number theory proposed
number theory
Problem Statement
Let
a
a
a
and
k
k
k
be positive integers such that
a
2
+
k
a^2+k
a
2
+
k
divides
(
a
−
1
)
a
(
a
+
1
)
(a-1)a(a+1)
(
a
−
1
)
a
(
a
+
1
)
. Prove that
k
≥
a
k\ge a
k
≥
a
.
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