MathDB

5

Part of 1999 Austrian-Polish Competition

Problems(1)

a_{n+1} = a_n^3 + 1999, exists at most 1 perfect square

Source: Austrian - Polish 1999 APMC

5/4/2020
A sequence of integers (an)(a_n) satisfies an+1=an3+1999a_{n+1} = a_n^3 + 1999 for n=1,2,....n = 1,2,.... Prove that there exists at most one nn for which ana_n is a perfect square.
recurrence relationSequencePerfect Squarenumber theory