MathDB

Pratyya and Payel have a number each,

n

and

m

respectively, where

n>m.

Everyday, Pratyya multiplies his number by

2

and then subtracts

2

from it, and Payel multiplies his number by

2

and then add

2

to it. In other words, on the first day their numbers will be

(2n-2)

and

(2m+2)

respectively. Find minimum integer

x

with proof such that if

n-m\geq x,

then Pratyya's number will be larger than Payel's number everyday.

Problem Statement