MathDB

5

Part of 2018 Caucasus Mathematical Olympiad

Problems(2)

Easy number theory

Source: III Caucasus Mathematical Olympiad

3/17/2018
Baron Munсhausen discovered the following theorem: "For any positive integers aa and bb there exists a positive integer nn such that anan is a perfect square, while bnbn is a perfect cube". Determine if the statement of Baron’s theorem is correct.
number theory
(another) easy number theory

Source: III Caucasus Mathematical Olympiad

3/17/2018
Baron Munсhausen discovered the following theorem: "For any positive integers aa and bb there exists a positive integer nn such that anan is a perfect cube, while bnbn is a perfect fifth power". Determine if the statement of Baron’s theorem is correct.
number theoryC.R.T