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show that the square of any positive integer is of the form of 8q+1,where q is the posotive integer
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show that the square of any positive integer is of the form of 8q+1,wh...
since any +ve odd integer n is of the form 4q+1 or 4q+3

if n = 4q+1

squaring both sides

n square= 16q2+1+ 8q

 8(2q2+1q)+1

  8q+1 where q=2q+1

if n=4q+3

squaring both sides

n square=16q2+9+24q

   8(2q2+1+3q)+1

 8q+1 where q=2q2+1+3q
 
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show that the square of any positive integer is of the form of 8q+1,where q is the posotive integer Related: Euclid's Division Lemma (Hindi) - Real Numbers, CBSE, Class 10, Mathematics
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