The set of integers can be classified into \( k \) classes, according to the remainder obtained ...

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The set of integers can be classified into \( k \) classes, according to the remainder obtained when they are divided by \( k \) (wherek is a fixed natural number). The classification enables is solving even some more difficult problems of number theory e.g.
(i) even, odd classification is based on whether remainder is 0 or 1 when divided by 2.
(ii) when divided by 3 , the remainder may be \( 0,1,2 \). Thus, there are three classes.
If \( n \) is odd, \( n^{5}-n \) is not divisible by
(a) 16
(b) 15
(c) 240
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