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Problems
Contests
National and Regional Contests
PEN Problems
PEN A Problems
76
76
Part of
PEN A Problems
Problems
(1)
A 76
Source:
5/25/2007
Find all integers
a
,
b
,
c
\,a,b,c\,
a
,
b
,
c
with
1
<
a
<
b
<
c
\,1<a<b<c\,
1
<
a
<
b
<
c
such that
(
a
−
1
)
(
b
−
1
)
(
c
−
1
)
is a divisor of
a
b
c
−
1.
(a-1)(b-1)(c-1)\hspace{0.2in}\text{is a divisor of}\hspace{0.2in}abc-1.
(
a
−
1
)
(
b
−
1
)
(
c
−
1
)
is a divisor of
ab
c
−
1.
Divisibility Theory