MathDB
Iran Second Round 2015 - Problem 6 day2

Source:

May 8, 2015
number theoryIranprime numbersalgebra

Problem Statement

Let n≥50n \ge 50 be a natural number. Prove that nn is expressible as sum of two natural numbers n=x+yn=x+y, so that for every prime number pp such that p∣x p\mid x or p∣yp\mid y we have n≥p \sqrt{n} \ge p . For example for n=94n=94 we have x=80,y=14x=80, y=14.
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