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Kvant 2021
M2657
M2657
Part of
Kvant 2021
Problems
(1)
NT about non-squarefree integers
Source: ARO 2021 10.7/9.7
4/20/2021
Given are positive integers
n
>
20
n>20
n
>
20
and
k
>
1
k>1
k
>
1
, such that
k
2
k^2
k
2
divides
n
n
n
. Prove that there exist positive integers
a
,
b
,
c
a, b, c
a
,
b
,
c
, such that
n
=
a
b
+
b
c
+
c
a
n=ab+bc+ca
n
=
ab
+
b
c
+
c
a
.
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