MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN A Problems
2
2
Part of
PEN A Problems
Problems
(1)
A 2
Source:
5/25/2007
Find infinitely many triples
(
a
,
b
,
c
)
(a, b, c)
(
a
,
b
,
c
)
of positive integers such that
a
a
a
,
b
b
b
,
c
c
c
are in arithmetic progression and such that
a
b
+
1
ab+1
ab
+
1
,
b
c
+
1
bc+1
b
c
+
1
, and
c
a
+
1
ca+1
c
a
+
1
are perfect squares.
arithmetic sequence
Diophantine equation
Divisibility Theory
Pell s Equation