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  • A positive integer is of the form 3q + 1, 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 mJustify your answer

A positive integer is of the form 3q + 1, 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

Answers (1)

Let us take the square of (3q + 1)                       

(3q + 1)2 = (3q) 2 + (1)2 + 2 × 3q × 1

 = 9q2 + 1 + 6q

= 9q2 + 6q + 1                                      

= 3(3q2 + 2q) + 1                     

= 3m + 1                                                  

{where m = 3q2 + 2q}

Hence, the square of 3q + 1 (where q is a positive integer) cannot be
written in any form other than 3m + 1
Hence the given statement is false.

Posted by

infoexpert27

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