MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
Harvard-MIT Mathematics Tournament
2016 Harvard-MIT Mathematics Tournament
17
17
Part of
2016 Harvard-MIT Mathematics Tournament
Problems
(1)
2016 Guts #17
Source:
12/24/2016
Compute the sum of all integers
1
≤
a
≤
10
1 \le a \le 10
1
≤
a
≤
10
with the following property: there exist integers
p
p
p
and
q
q
q
such that
p
p
p
,
q
q
q
,
p
2
+
a
p^2+a
p
2
+
a
and
q
2
+
a
q^2+a
q
2
+
a
are all distinct prime numbers.