CBSE Guess Official Helpline Forum for CBSE Students, Teachers and Parents. Educational Portals: ICSE | IGNOU | NIOS | IIT JEE | AIPMT | AIEEE | Friends

IMPORTANT INFORMATION: To participate in this form you need to register as your CBSEGuess.com login info will not work here. Click Here to Register

Ask questions of CBSE Class X and discuss the same here. For any doubts relates to CBSE Class X.

Question. Use Euclid"s division lemma to show that the square of any positive integer is either of the form 3m or 3m+1.
[Hint: x be any positive integer then it is of the form 3q, 3q+1 or 3q+2. Now square of these and show that they can be rewritten in the form 3m or 3m+1.]

Ans. An integer can be of the form 3q, 3q+1 or 3q+2. Square all of these integers.
Shrestha

Posts: 5
Joined: Thu Mar 12, 2009 7:05 pm

let a b any +ve integer and let b= 3.
using euclid's div. algorithm, a= bq+r or a= 3q+r, where 0 is less thn or equal to r which is less thn b.
therefore, r can take values: 0, 1, 2 (since b=3)

for, r=0:
a= 3*q + 0
a= 3q
a= 3m (where q is some integer, m)

for, r= 1
a= 3*q + 1
a= 3q + 1
a= 3m + 1 (where q is some integer m)

v can also take our (3m+2), but we won't.... since it is not asked in quesion..
shubhangi_d23

Posts: 2
Joined: Fri Oct 23, 2009 10:49 am 