Find All Unfaithful | Indian Math Olympiad 2011 | Math Olympiad Training

Call a natural number n faithful, if there exist natural numbers a, b and c such that a is less than b, and b is less than c. Where a|b, 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.

The Indian National Mathematical Olympiad (INMO) is a high school mathematics competition held annually in India since 1989. It is the third tier in the Indian team selection procedure for the International Mathematical Olympiad.

The qualifying students are invited to the International Mathematical Olympiad Training Camp (IMOTC), a one-month mathematics camp hosted by the Homi Bhabha Centre for Science Education in Mumbai. In this camp, the students are taught Olympiad mathematics and some other general mathematics. Four selection tests and two practice tests are held during this period and the top six students in the selection tests qualify to represent India in the International Mathematical Olympiad.

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[MaxMathGames]

That was an easy one
And well explained

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