Question

show that any positive odd integer is in the form of 6q + 1 or 6q + 3 or 6q + 5 Where Q is some integer

Answer 1

by Euclid division lemma
let a= bq+r where b= 6
so r=0,1,2,3,4,5
so any positive odd integer is of the form
a=6q+1 or 6q+3 or 6q+5 .....


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Answer 2

HEY FRIEND HERE IS UR ANSWER,

Let a be any positive integer and b = 6. Then, by Euclid’s algorithm, a = 6q + r, for some integer q ≥ 0, and r = 0, 1, 2, 3, 4, 5, because 0≤r<6.

Now substituting the value of r, we get,

If r = 0, then a = 6q

Similarly, for r= 1, 2, 3, 4 and 5, the value of a is 6q+1, 6q+2, 6q+3, 6q+4 and 6q+5, respectively.

If a = 6q, 6q+2, 6q+4, then a is an even number and divisible by 2. A positive integer can be either even or odd Therefore, any positive odd integer is of the form of 6q+1, 6q+3 and 6q+5, where q is some integer.

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