MathDB
Problems
Contests
National and Regional Contests
Russia Contests
239 Open Math Olympiad
2022 239 Open Mathematical Olympiad
5
5
Part of
2022 239 Open Mathematical Olympiad
Problems
(1)
Problem 5
Source: 239-School Open Olympiad (Senior Level)
4/25/2022
Prove that there are infinitely many positive integers
k
k
k
such that
k
(
k
+
1
)
(
k
+
2
)
(
k
+
3
)
k(k+1)(k+2)(k+3)
k
(
k
+
1
)
(
k
+
2
)
(
k
+
3
)
has no prime divisor of the form
8
t
+
5.
8t+5.
8
t
+
5.
number theory
primes