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Question

Show that square of an odd positive integer can be of the from 6q+1 or 6q+3 for some integer q.

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Solution

(6q+1)or(6q+3)qIA/Ctodivisionaorithamaandbarepositiveintegersa=bq+r0r<ba=6q+r0r<6r=0,1,2,3,4,5Becauseoddpositiveintegerareconsider

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