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4

Part of PEN M Problems

Problems(1)

M 4

Source:

5/25/2007
The sequence {an}n≥1 \{a_{n}\}_{n \ge 1} is defined by a1=1,  a2=2,  a3=24,  an=6an−12an−3−8an−1an−22an−2an−3    (n≥4). a_{1}=1, \; a_{2}=2, \; a_{3}=24, \; a_{n}=\frac{ 6a_{n-1}^{2}a_{n-3}-8a_{n-1}a_{n-2}^{2}}{a_{n-2}a_{n-3}}\ \ \ \ (n\ge4). Show that an a_{n} is an integer for all n n, and show that n∣an n|a_{n} for every n∈N n\in\mathbb{N}.
EulerRecursive Sequences