Let x_1 be a positive real number and for every integer n ≥ 1 let x_ n+1 =1+x_1 x_2 x_ n-1 x_n . If x_5=43 , what is the sum of digits of the largest prime factor of x_6 ?

Correct answer: 13 array ll x_5=1+x_1 x_2 x_3 x_4 & x_1 x_2 x_3 x_4=42 x_6=1+x_1 x_2 x_3 x_4 x_5 & =1+(42)(43)=1807=13 × 139 array largest prime factor =139 sum of digits =13

Olympiad workbook

Exam: Olympiad workbook
Subject: IOQM
Chapter: Functions

Olympiad workbook · IOQM · Functions

Let x_1 be a positive real number and for every integer n ≥ 1 let...

Let

x_1

be a positive real number and for every integer

n \geq 1

let

x_{n+1}=1+x_1 x_2 \ldots \ldots x_{n-1} x_n

. If

x_5=43

, what is the sum of digits of the largest prime factor of

x_6

Correct answer

Step-by-step solution

\begin{array}{ll} x_5=1+x_1 x_2 x_3 x_4 & \Rightarrow x_1 x_2 x_3 x_4=42 \\ x_6=1+x_1 x_2 x_3 x_4 x_5 & =1+(42)(43)=1807=13 \times 139 \end{array}

\Rightarrow

largest prime factor

=139 \Rightarrow

sum of digits

=13

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