Question

show that any positive odd integer is in the form 6p+1, 6p+3 or 6p+5 where p is some integer

Answer 1

Here's your answer...


By Euclid division lemma...


a = bq+r


Here,


b is 6


And r should be less than 6


r = (1,2,3,4,5,6)


a = bq+r


If r = 0


a = 6q +0It is even... because it is divisible by 2


If r = 1


a = 6q+1It is odd... because it is not divisible by 2


If r = 2


a = 6q+2It is even...it is divisible by 2


If r = 3


a = 6q+3It is odd... because it is not divisible by 2


If r =4


a = 6q+4It is even... because it is divisible by 2


If r = 5


a = 6q + 5It is odd.. because it is not divisible by 2


So...


Any positive odd integer will be in the form of 6q+1 or 6q + 3 or 6q + 5



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