Question

show that the square of odd positive integer can be of the form 6q + 1 are 6 q + 3 for some integer q​

Answer 1

Using Euclid’s division algorithm,we have

x=bq+r {0≤r<b}…..(1)

Substituting b=6in equation(1)

So, x=6q+r,where r=0,1,2,3,4,5

If r=0, x=6q+0(divisible by 2)…..even

r=1, x=6q+1(not divisible by 2)…..odd

r=2, x=6q+2(divisible by 2)…..even

r=3, x=6q+3(not divisible by 2)…..odd

r=4, x=6q+4(divisible by 2)…..even

r=5, x=6q+5(not divisible by 2)…..odd

Therefore,the number 6q,6q+1,6q+2,6q+3,6q+4,6q+5are either even or odd.Hence ,any positive odd integer is of the form 6q+1,6q+3 & 6q+5Where q is some integer.

mark as brainlist please.... thanks