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Use Euclid's division lemma to show that they possess ofthe form 3m or 3m + 1 for some integer m. |
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Answer» Let a be any possitive integer and b=3. By eucluds division LEMMA, a=3c+r where r=0,1,2 Case I- a=3c a²=9c²=3(3c²)=3m Case II-a=3c+1 a²=9c²+6c+1=3(3c²+2c)+1=3m+1 Case III-a=3c+2 a²=9c²+6c+4=9c²+6c+3+1=3(3c²+2c+1)+1=3m+1 Therefore square of any possitive integer is of the form 3m or 3m+1. Now let me help you in judging why I started with a and not directly with a².This is because of the language of question.The question SAYS square of a possitive integer which IMPLIES that first we have to take the possitive integer and then square it. To check your understanding,TRY to prove The cube of a possitive Integer is of the form of 9m,9m+1,9m+8.(HINT-Read language of question)
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