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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by euclids division lemma a = bq + r
where b = 6 in this case
so possible nos are 0,1,2,3,4,5
when r = 0 nos. = 6q = 2(3q) ...................even nos.
r = 1 = 6q+1 = 2(3q)+1 ............................odd nos
r=2 6q +2 = 2(3q+1) .................................even nos
r=3 6q+3 = 2(3q)+3..................................odd nos
r=4 6q+4 = 2 (3q+2) ...............................even nos
r= 5 6q+5 = 2(3q)+5 ..............................odd nos
Hence positive odd integer is in the form of 6q+1 , 6q+3 , 6q+5 for some integer q
Hope this helps you
Thank you .
where b = 6 in this case
so possible nos are 0,1,2,3,4,5
when r = 0 nos. = 6q = 2(3q) ...................even nos.
r = 1 = 6q+1 = 2(3q)+1 ............................odd nos
r=2 6q +2 = 2(3q+1) .................................even nos
r=3 6q+3 = 2(3q)+3..................................odd nos
r=4 6q+4 = 2 (3q+2) ...............................even nos
r= 5 6q+5 = 2(3q)+5 ..............................odd nos
Hence positive odd integer is in the form of 6q+1 , 6q+3 , 6q+5 for some integer q
Hope this helps you
Thank you .
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