Question

show that the positive odd integer is of the form 4q + 1 or 4 Cube + 3 where Q is some integer​

Answer 1

Answer:

let a be any positive integer and b=4,by Euclid division lemma ,a=4q+r,0 g

less than equal to q less than r

therefore,r=0,1,2,3

now,a=4q(when r=0)

a=4q+1(when r=1)

a=4q+2(when r=2)

a=4q+3(when r=3)

so, 4q and 4q+2 are even number

hence, the positive odd integer can be of the form 4q+1 or 4q +3.