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