MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - Other Middle and High School Contests
Purple Comet Problems
2016 Purple Comet Problems
24
24
Part of
2016 Purple Comet Problems
Problems
(1)
Purple Comet 2016 HS Problem 24
Source:
4/12/2018
Find the largest prime
p
p
p
such that
p
p
p
divides
2
p
+
1
+
3
p
+
1
+
5
p
+
1
+
7
p
+
1
2^{p+1} + 3^{p+1} + 5^{p+1} + 7^{p+1}
2
p
+
1
+
3
p
+
1
+
5
p
+
1
+
7
p
+
1
.
Purple Comet