MathDB

3

Part of 2019 India PRMO

Problems(2)

Simple Recurrence solving

Source:

8/11/2019
Let x1x_{1} be a positive real number and for every integer n≥1n \geq 1 let xn+1=1+x1x2…xn−1xnx_{n+1} = 1 + x_{1}x_{2}\ldots x_{n-1}x_{n}. If x5=43x_{5} = 43, what is the sum of digits of the largest prime factors of x6x_{6}?
Recurrencerecursion
Difference of squares

Source: PRMO 2019 Leg 2 P3

8/25/2019
Find the number of positive integers less than 101 that can not be written as the difference of two squares of integers.
PRMOnumber theoryalgebradifference of squaresspecial factorizations