8

Part of 2002 AIME Problems

Problems(2)

Source:

Find the smallest integer

k

for which the conditions

(1)

a_1, a_2, a_3, \ldots

is a nondecreasing sequence of positive integers

(2)

a_n=a_{n-1}+a_{n-2}

n>2

(3)

a_9=k

are satisfied by more than one sequence.

number theoryrelatively prime2002 AIME I 8

Floor Function Skipping Integers

Source:

Find the least positive integer

k

for which the equation

\lfloor \frac{2002}{n}\rfloor = k

has no integer solutions for

n.

\lfloor x \rfloor

means the greatest integer less than or equal to

x.

functionfloor functionparameterizationalgebra