MathDB

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Part of 2016 Latvia National Olympiad

Problems(4)

2016 Latvia National Olympiad 3rd Round Grade9Problem1

Source:

7/22/2016
Given positive integers xx and yy such that xy2xy^2 is a perfect cube, prove that x2yx^2y is also a perfect cube.
number theory
2016 Latvia National Olympiad 3rd Round Grade10Problem1

Source:

7/22/2016
Given that xx and yy are positive integers such that xy10xy^{10} is perfect 33rd power of a positive integer, prove that x10yx^{10}y is also a perfect 33rd power!
number theory
2016 Latvia National Olympiad 3rd Round Grade11Problem1

Source:

7/22/2016
Given that xx and yy are positive integers such that xy433xy^{433} is a perfect 2016-power of a positive integer, prove that x433yx^{433}y is also a perfect 2016-power.
number theoryPerfect Powers
2016 Latvia National Olympiad 3rd Round Grade12Problem1

Source:

7/22/2016
Given that xx, yy and zz are positive integers such that x3y5z6x^3y^5z^6 is a perfect 7th power of a positive integer, show that also x5y6z3x^5y^6z^3 is a perfect 7th power.
number theoryPerfect Powers