MathematicsState whether this is true or false.The square of any odd is of the form  for some integer .

State whether this is true or false.


The square of any odd is of the form  for some integer .


  1. A
    True
  2. B
    False 

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    Solution:

    Let, a be any odd number,
    B=4,
    By Euclid’s algorithm, For some integer , because .
    When ,
    Now square both sides, we get:
    When ,
    Now square both sides, we get:
    When ,
    Now square both sides, we get:
    When ,
    Now square both sides, we get:
     Hence, Square of any positive integer is in the form of 4q or 4q + 1, where q is any integer.
    So, the given statement is true.
     
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