Question

Show that any positive even inteser is of the form 8q+2 or 8q+4 or 8q+6 where q is some inteset

Answer 1

Answer:

Step-by-step explanation:

by euclid's division lemma, a=8q+r, and r=0,1,2,3,4,5,6,7

when r=0,a=8q even

when r=1, a=8q+1 odd

r=2, a=8q+2 even

r=3, a=8q+3 odd

r=4, a=8q+4 even

r=5, a=8q+5 odd

r=6, a=8q+6 even

r=7, a=8q+7 odd

hence proven