Question

show that the squares of any positive integer is either of the form 4q or 4q+1 for some integer q​

Answer 1

Answer:

Step-by-step explanation:

a = bq + r

b = 4

a = 4q + r

where 0≤b<r

hence possible values of r = 0,1,2,3

putting value of r's we get

1. a=4q + 0

   = 4(q)

   =4m                                    (where m refers to multiple)

2. a=4q+1

    =4(q)+1

    =4m+ 1                                 (              "             )

3. a=4q+2

     =4(q+1/2)

     = 4m                                    (              "             )

4. a=4q + 4

     = 4(q+1)

     =4m                                     (              "             )

hence proved squares of any positive integer is either of the form 4q or 4q+1 for some integer q​

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MARK AS BRAINLIEST