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Show that the square of positive integer is either of the form 6 Q + 1 or 6q + 3 |
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Answer» LET the REMAINDERS be 0,1,2,3,4,5 r=0 =6 r=1 (6q+1)2 36q2+1-12q 6q(6-2)+1 6q+1 r=2 (6q+2)2 36q2+4-24q 6q(6-4) +4 6q+4 r=3 (6q+3)2 36q2+9-36q 6q(6-6)+9 6q+9 r=4 (6q+4)2 36q2+16+48q 6q(6-8)+16 6q+16 r=5 (6q+5)2 36q2+25-60q 6q(6-10)+25 6q+25 |
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