Question

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Show that any positive odd integer is of the form 6q+1, or 6q+3, or 6q+5 , where q is some integer.

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Answer 1

hlo mate your answer


Let 'a' be any positive odd integer. and b=6.

Let 'q' be quotient and 'r' be remainder.

a=6q+r where 0≤r<6

or a=6q+0

or a=6q+1

or a=6q+2

or a=6q+3

or a=6q+4

or a=6q+5

=> r=0,1,2,3,4,5

But Now, here odd integer are 6q+1, 6q+3, and 6q+5

Hence proved that any odd integer is of the form 6q+1, 6q+3 and 6q+5

Hope it helps!