MathDB

4

Part of 1985 Poland - Second Round

Problems(1)

\sqrt[3]{a} + \sqrt[3]{b} is rational

Source: Polish MO Recond Round 1985 p4

9/9/2024
Prove that if for natural numbers a,b a, b the number a3+b3 \sqrt[3]{a} + \sqrt[3]{b} is rational, then a,b a, b are cubes of natural numbers.
algebrarationalradicalnumber theoryperfect cube