Baltic Way 1992 · Problem 2
Number Theory
Denote by the number of all positive divisors of a positive integer (including 1 and ). Prove that there are infinitely many such that is an integer.
When you’re ready
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Review
Topics
Primes · Divisibility and factorization · Arithmetic functions
Solutions
Solution
Solution:
Consider numbers of the form where is an arbitrary prime number and
Contest context
Results from Baltic Way 1992
8 teams
- Mean score
- 4.4 / 5
- Scores of 4 or 5
- 7 / 8
- Estonia
- 5 / 5
Score distribution
01
10
20
30
40
57
All team scores
| Team | Score |
|---|---|
| Denmark | 5 / 5 |
| St. Petersburg | 5 / 5 |
| Poland | 5 / 5 |
| Latvia | 5 / 5 |
| Iceland | 0 / 5 |
| Lithuania | 5 / 5 |
| Estonia | 5 / 5 |
| Sweden | 5 / 5 |