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National and Regional Contests
Indonesia Contests
Indonesia MO Shortlist
2015 Indonesia MO Shortlist
N1
N1
Part of
2015 Indonesia MO Shortlist
Problems
(1)
min of abc when a>b>b, primes, a=b+2c, a + b + c is perfect square
Source: INAMO Shortlist 2015 N1
5/14/2019
A triple integer
(
a
,
b
,
c
)
(a, b, c)
(
a
,
b
,
c
)
is called brilliant when it satisfies: (i)
a
>
b
>
c
a> b> c
a
>
b
>
c
are prime numbers (ii)
a
=
b
+
2
c
a = b + 2c
a
=
b
+
2
c
(iii)
a
+
b
+
c
a + b + c
a
+
b
+
c
is a perfect square number Find the minimum value of
a
b
c
abc
ab
c
if triple
(
a
,
b
,
c
)
(a, b, c)
(
a
,
b
,
c
)
is brilliant.
number theory
Perfect Square
triplets
primes