Question

Use Euclid division lemma to show that the square of any positive inter is of form 8m+1 for some integer m . ​

Answer 1

Answer:

Step-by-step explanation:

let a and b be any positive interger such that a>b

then by  Euclid division lemma

a=bq + r

where b=4 and 0≤r<b

therefore

a=4q+0  ,   a=4q+1   ,   a=4q+2  ,  a=4q+3  

consider a=4q+1

               a²=( 16q² +8q +1)

               a²=8(2q² +q) +1

let m be = 2q² +q  

 therefore, a²=8m+1

  the square of any positive inter is of form 8m+1 for some integer m . ​