Baltic Way 1993 · Problem 3

Number Theory

Let's call a positive integer "interesting" if it is a product of two (distinct or equal) prime numbers. What is the greatest number of consecutive positive integers all of which are "interesting"?

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Topics

Primes · Divisibility and factorization

Solutions

Solution

Solution:

The three consecutive numbers $33 = 3 \cdot 11$ , $34 = 2 \cdot 17$ and $35 = 5 \cdot 7$ are all "interesting". On the other hand, among any four consecutive numbers there is one of the form $4k$ which is "interesting" only if $k = 1$ . But then we have either $3$ or $5$ among the four numbers, neither of which is "interesting".

Contest context

Results from Baltic Way 1993

8 teams

Mean score: 5.0 / 5
Scores of 4 or 5: 8 / 8
Estonia: 5 / 5

Score distribution

All team scores

Team	Score
Poland	5 / 5
Latvia	5 / 5
Estonia	5 / 5
Sweden	5 / 5
Lithuania	5 / 5
Finland	5 / 5
Iceland	5 / 5
Denmark	5 / 5

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