Question

Show that any positive odd integer is of the form 6q+1, or 6q+3, or 6q+5, where q is
some integer
​

Answer 1

Answer:

Using Euclid division algorithm, we know that a=bq+r, 0≤r≤b ----(1)

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 ,or 0≤r<6.

Therefore, a=6qor6q+1or6q+2or6q+3or6q+4or6q+5

6q+0:6 is divisible by 2, so it is an even number.

6q+1:6 is divisible by 2, but 1 is not divisible by 2 so it is an odd number.

6q+2:6 is divisible by 2, and 2 is divisible by 2 so it is an even number.

6q+3:6 is divisible by 2, but 3 is not divisible by 2 so it is an odd number.

6q+4:6 is divisible by 2, and 4 is divisible by 2 so it is an even number.

6q+5:6 is divisible by 2, but 5 is not divisible by 2 so it is an odd number.

And therefore, any odd integer can be expressed in the form 6q+1or6q+3or6q+5

Answer 2

Answer:

good morning sister

have a great day ahead and

:) good day

Step-by-step explanation:

i could not answer in the first question

cause it was occupied by others

so I answered from here itself

I will not waste this question

a=bq+r 0≤r<b

b=6

r=1,2,3,4,5,6,∞

therefore a=6q+1 ✓

a=6q+2

a=6q+3✓

a=6q+4

a=6q+5✓

a=6q+6

that is your answer hope it is helpful