4

Part of 2019 Auckland Mathematical Olympiad

Problems(2)

a_n = a_{n-1} - 1/n+ 1/(n + 1) - 1/(n + 2) (2019 Auckland MO J4)

Source:

a_1 =\frac16

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

n > 1

a_{100}

algebraSequence

min pos. integer not in form (2^a - 2^b/(2^c - 2^d) (2019 Auckland MO S4)

Source:

Find the smallest positive integer that cannot be expressed in the form

\frac{2^a - 2^b}{2^c - 2^d}

a

b

c

d

are non-negative integers.