+1 vote
in Mathematics by (105k points)

A positive integer is of the form 3q + 1, q being a natural number. Can you write its square in any form other than 3m + 1, i.e., 3m or 3m + 2 for some integer m? Justify your answer.

1 Answer

+2 votes
by (24.0k points)
selected by
Best answer

Consider the positive integer 3q + 1, where q is a natural number.
=> (3q + 1)2 = 9q2 + 6q + 1
= 3(3q2 + 2q) + 1
= 3m + 1, where m is an integer.
Thus (3q + 1)2 cannot be expressed in any other form apart from 3m + 1.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.