11.9

Part of V Soros Olympiad 1998 - 99 (Russia)

Problems(2)

a_{n+1}=\frac{k+a_n}{1-a_n} (V Soros Olympiad 1998-99 Round 1 11.9)

Source:

The sequence of

a_n

is determined by the relation

a_{n+1}=\frac{k+a_n}{1-a_n}

k > 0

. It is known that

a_{13} = a_1

. What values can

k

Recurrencerecurrence relationSequencealgebra

squares in arithm. progression (V Soros Olympiad 1998-99 Round 3 11.9)

Source:

It is known that unequal numbers

a

b

c

are successive members of an arithmetic progression, all of them are greater than

1000

and all are squares of natural numbers. Find the smallest possible value of

b

algebranumber theory