Daniel J Smith Custom TMUA Set A Paper 1 · Question 17

Let $a$ and $b$ be positive integers and define a sequence $v_n$ by

v_1=a,\quad v_2=b,\quad v_{n+2}=2v_{n+1}-v_n\quad\text{for }n\geq1

Suppose the highest common factor of $a$ and $b$ is $d$

Which of the following statements must be true?

AThe highest common factor of

v_{10}

and

v_{11}

1

v_n

is divisible by

d

only for even

n

CThe highest common factor of

v_n

and

v_{n+1}

d

for all

n\geq1

DFor all

n\geq1

v_n

is divisible by

2d

EIf

a\neq b

then

v_n

is never divisible by

d

examday