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Problems
Contests
National and Regional Contests
Korea Contests
Korea Junior Mathematics Olympiad
2009 Korea Junior Math Olympiad
1
1
Part of
2009 Korea Junior Math Olympiad
Problems
(1)
find abc when a\(b+8), a\(b^2 - 1), c\(b^2 - 1), b + c = a^2-1, primes a,b,c
Source: KJMO 2009 p1
5/2/2019
For primes
a
,
b
,
c
a, b,c
a
,
b
,
c
that satis fy the following, calculate
a
b
c
abc
ab
c
.
∙
\bullet
∙
b
+
8
b + 8
b
+
8
is a multiple of
a
a
a
,
∙
\bullet
∙
b
2
−
1
b^2 - 1
b
2
−
1
is a multiple of
a
a
a
and
c
c
c
∙
\bullet
∙
b
+
c
=
a
2
−
1
b + c = a^2 - 1
b
+
c
=
a
2
−
1
.
number theory
multiple
Product
primes