MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN A Problems
52
52
Part of
PEN A Problems
Problems
(1)
A 52
Source:
5/25/2007
Let
d
d
d
be any positive integer not equal to 2, 5, or 13. Show that one can find distinct
a
a
a
and
b
b
b
in the set
{
2
,
5
,
13
,
d
}
\{2,5,13,d\}
{
2
,
5
,
13
,
d
}
such that
a
b
ā
1
ab - 1
ab
ā
1
is not a perfect square.
quadratics
modular arithmetic
Divisibility Theory
pen