Saved Bookmarks
| 1. |
show that the square of any positive integer cannot be of the form 6 m + 2 or 6 m + 5 for any Integer |
|
Answer» Answer: Let the positive integer be a and b=6. According to Euclid's DIVISION lemma, a=bq+r Here, a=6q+4 where 0 So possible values of r are 0, 1,2,3,4,5 CASE1. when r=0, a=4 a^2 =16 a^2 =6(2)+4 a^2 =6m+4..............equation1 CASE 2.r=1, a=10 a=6m+4(m=1).................eq2 CASE3.a=6m+4(m=2)....... ........................... Similarly do for case4, 5 and 6.YOU WILL NOT GET a=6m+2 or 6m+5. At last write down.. Hence, the square of any posit integer the cannot be of the FORM 6m+2 or 6m+5 for any integer m |
|