Question

3. W 20 Show that any positive odd integer is of the from 69 + 1, or 64+3, or 64+5, where q is some integer.

Bank Exams

Maths

Solution

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Let a be the positive odd integer which when divided by 6 gives ( q ) as quotient and ( r ) as remainder. according to Euclid's division lemma ( a=b q+r ) ( a=6 q+r ) where ( , a=0,1,2,3,4,5 ) then, ( a=6 q ) Or ( a=6 q+1 ) Or ( a=6 q+2 ) Or ( a=6 q+3 ) Or ( a=6 q+4 ) Or ( a=6 q+5 ) but here, ( a=6 q+1 & a=6 q+3 & a=6 q+5 ) are odd