Question
Sun April 18, 2010 By: Ankit Khound

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

Expert Reply
Tue April 20, 2010

Let a  be any odd positive intger and b =6. applying Euclid's Lemma  to and b we get

a =6q,6q+1,6q+2,6q+3,6q+4 6q+5  where q is quotient.

Since a is odd so a cannot take values 6q and 6q+2,6q+4.

So a =6q+1,6q+3,6q+5

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