Question

show that square of any positive integer is of the form 4m ,4m+2,where m is any integer

Answer 1

let 4q , 4q+1 be any positive integer 

x = 4q

squaring both sides 

x square = 16q square

x square = 4(4q square)

put 4q square be m 

x = 4m

also 4q+1 =x

squaring both sides

x square = 16q square +1 +8q 

x = 4(4q square + 2q) +1

put 4q square + 2q = m

x = 4m +1

Hence proved

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