MathDB

Problem 2

Part of 2001 Slovenia National Olympiad

Problems(4)

Pairwise sums given, find numbers (Slovenia National MO 2001 1st Grade P2)

Source:

4/7/2021
Tina wrote a positive number on each of five pieces of paper. She did not say which numbers she wrote, but revealed their pairwise sums instead: 17,20,28,14,42,36,28,39,25,3117,20,28,14,42,36,28,39,25,31. Which numbers did she write?
Inequalityalgebra
sum of product of digits

Source: Slovenia National MO 2001 2nd Grade P2

4/5/2021
Let p(n)p(n) denote the product of decimal digits of a positive integer nn. Computer the sum p(1)+p(2)+…+p(2001)p(1)+p(2)+\ldots+p(2001).
number theory
rational parameter, integral solutions (Slovenia National MO 2001 3rd Grade P2)

Source:

4/7/2021
Find all rational numbers rr such that the equation rx2+(r+1)x+r=1rx^2 + (r + 1)x + r = 1 has integer solutions.
Quadratic
3^p-(p+2)^2 prime (Slovenia National MO 2001 4th Grade P2)

Source:

4/7/2021
Find all prime numbers pp for which 3p−(p+2)23^p-(p+2)^2 is also prime.
number theory