MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN E Problems
36
E 36
E 36
Source:
May 25, 2007
Problem Statement
Prove that there are infinitely many twin primes if and only if there are infinitely many integers that cannot be written in any of the following forms:
6
u
v
+
u
+
v
,
6
u
v
+
u
−
v
,
6
u
v
−
u
+
v
,
6
u
v
−
u
−
v
,
6uv+u+v, \;\; 6uv+u-v, \;\; 6uv-u+v, \;\; 6uv-u-v,
6
uv
+
u
+
v
,
6
uv
+
u
−
v
,
6
uv
−
u
+
v
,
6
uv
−
u
−
v
,
for some positive integers
u
u
u
and
v
v
v
.
Back to Problems
View on AoPS