Question

show that any positive odd integer is of the form 6q+1,or 6q+3 or 6q+5 for some integer

Answer 1

a=bq+r

6q-even

6q+1-odd

6q+2-even

6q+3-odd

6q+4-even

6q+5-odd

from the above statement we know that 6q+1,6q+3,6q+5 will be in the odd form where q is some integer

Answer 2

Answer:

Here is ur answer

Step-by-step explanation:

Let a be any positive integer and b=6 then by Euclid Algorithm

a=6q+r

Then possible values of r=0,1,2,3,4,5

r=0 6q+0 a=6q(even)

r=1 6q+1 a=6x2+1=13(odd)

r=2 6q+2 a=6x2+2=14(odd)

r=3 6q+3 a=6x2+3=15(even)

r=4 6q+4 a=6x2+4=16(odd)

r=5 6q+5 a=6x2+5=17(odd)

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