show that any positive odd integer is of the form 6q+1,or6q+3,or 6q+5 where q is some integer.
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nish2741996:
will u tell me that if we solve eculid's division lemma; so is it compulsory to write theoretical part
yeah it is.
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on dividing 'p' by 6 let 'r' be the remainder and 'q' be the quotient.
then
r=0,1,2,3,4,5
(1)case 1 :-
r=0
p =6q
(2) case 2
r=1
p=6q+1
(3) r=2
p= 6q+2
(4) r=3
p= 6q+3
(5) r=4
p=6q+4
(6) r=5
p=6q+5
this shows that any positive odd integer is of the form 6q+1, 6q+3, 6q+5 for some integer q.
then
r=0,1,2,3,4,5
(1)case 1 :-
r=0
p =6q
(2) case 2
r=1
p=6q+1
(3) r=2
p= 6q+2
(4) r=3
p= 6q+3
(5) r=4
p=6q+4
(6) r=5
p=6q+5
this shows that any positive odd integer is of the form 6q+1, 6q+3, 6q+5 for some integer q.
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