MathDB

5

Part of 1989 Poland - Second Round

Problems(1)

c_{n+1} = [ 3/2 c_n ]

Source: Polish MO Recond Round 1989 p5

9/9/2024
Given a sequence (cn) (c_n) of natural numbers defined recursively: c1=2 c_1 = 2 , cn+1=[32cn] c_{n+1} = \left[ \frac{3}{2}c_n\right] . Prove that there are infinitely many even numbers and infinitely many odd numbers among the terms of this sequence.
algebrarecurrence relationfloor functionnumber theory