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Bosnia and Herzegovina JBMO TST 2009 Problem 3

Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2009

September 17, 2018
number theoryprimeDivisionprime numbers

Problem Statement

Let pp be a prime number, p≠3p\neq 3 and let aa and bb be positive integers such that p∣a+bp \mid a+b and p2∣a3+b3p^2\mid a^3+b^3. Show that p2∣a+bp^2 \mid a+b or p3∣a3+b3p^3 \mid a^3+b^3
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