Question

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

Answer 1

Step-by-step explanation:

let,

a is a positive integer and b=6 for any positive integers q we have by Euclid's divisions lemma.

a= 6q+r

then r=0,1,2,3,4,5

a=6q+0=2x3q= even

a=6q+1=2x3q+1= odd

a=6q+2=2x3q+2=even

a=6q+3=2x3q+3=odd

a=6q+4=2x3q+4= even

a=6q+5=2x3q+5= odd

•°• any +ve odd integers is of the form 6q+1,6q+3 and 6q+5.