This is I.S.I. 2015 Subjective 2 Solution (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.
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Find all such Natural number n such that 7 divides
Teacher: This is simple case of modular arithmetic. Consider the set of all residues of modulo 7 and you will see a pattern
Student: Sure. modulo 7. The residues repeat after that since modulo 7 where .
We want mod 7 hence n must be an odd multiple of 3 or n = 6r + 3 for any nonnegative integer r.