MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN A Problems
75
75
Part of
PEN A Problems
Problems
(1)
A 75
Source:
5/25/2007
Find all triples
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
of positive integers such that
2
c
ā
1
2^{c}-1
2
c
ā
1
divides
2
a
+
2
b
+
1
2^{a}+2^{b}+1
2
a
+
2
b
+
1
.
modular arithmetic
Divisibility Theory