1
Problems(2)
Prime sequence
Source: 239 2009 J2
7/29/2020
In a sequence of natural numbers, the first number is , and each subsequent number is the smallest number coprime to all the previous ones and greater than all of them. Prove that in this sequence from some place all numbers will be primes.
number theorySequence
Interesting roads
Source: 239 2009 J1
7/29/2020
Kostya drives a car from a village to a city, driving along three roads. Moreover, on each of these roads, he drives at a constant speed. Is it possible that a third of the distance traveled was completed earlier than a third of the time, half of the distance traveled later than half of the time, and two-thirds of the distance was earlier than two-thirds of the time?