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A number n is faithful if n=a+b+c, a|b, b|c-[INMO 2011]

Source:

February 6, 2011

number theory proposednumber theory

Problem Statement

Call a natural number

n

faithful if there exist natural numbers

a<b<c

such that

a|b,

and

b|c

and

n=a+b+c.

(i)

Show that all but a finite number of natural numbers are faithful.

(ii)

Find the sum of all natural numbers which are not faithful.