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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## Problem

Find all such Natural number n such that 7 divides

## Discussion:

**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.

so ashani sir i could do the sum in following way that if i write 5 as (7-2)^n and expand it binomially then we have a term indepent of 7 and that term if i calculate so it would give me the answer possibly.

Hmm it would … But then you have to check that term mod 7

yes that term mod 7 will give us the remainder part which is not a multiple of 7 and in that part if we put value of n i think probably 2 i dont remember as in paper i have done and that would give the term multiple of 7 and so we will get its value mean the value of n

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How much marks are required in paper2 of b.maths???