MathDB
Problems
Contests
International Contests
Baltic Way
2016 Baltic Way
2
2
Part of
2016 Baltic Way
Problems
(1)
Two conjectures
Source: Baltic Way 2016, Problem 2
11/5/2016
Prove or disprove the following hypotheses. a) For all
k
≥
2
,
k \geq 2,
k
≥
2
,
each sequence of
k
k
k
consecutive positive integers contains a number that is not divisible by any prime number less than
k
.
k.
k
.
b) For all
k
≥
2
,
k\geq 2,
k
≥
2
,
each sequence of
k
k
k
consecutive positive integers contains a number that is relatively prime to all other members of the sequence.
number theory