Show that any postive odd interer is of the form 6q+1 or 6q+3or 6q+5,where q is some interger
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let a be a positive integer
b=6
possible remInders =1,2,3,4,5
a=bq+r
a=6q+1= 6q+1=2n+1= odd
a=6q+2=2(3q+1)=2n=even
a=6q+3=2(3q+1)+1=2+1=odd
a=6q+4=2(3q+2)=2n=even
a=6q+5=2(3q+2)+1=odd
therefore,6q+1,6q+3,6q+5 are positive odd integers
b=6
possible remInders =1,2,3,4,5
a=bq+r
a=6q+1= 6q+1=2n+1= odd
a=6q+2=2(3q+1)=2n=even
a=6q+3=2(3q+1)+1=2+1=odd
a=6q+4=2(3q+2)=2n=even
a=6q+5=2(3q+2)+1=odd
therefore,6q+1,6q+3,6q+5 are positive odd integers
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