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se Euclid division lemma to show that any positive odd integer is of the form 63or 6q +5, where q is some integers. |
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Answer» Use Euclid's division lemma to show that any positive odd integer is of the form 6q+1,6q+3,6q+5 where q is a certain integer. Answer:-Let a be a positive odd integer a=bq+rb=6 a=6q+r, 0≤r<6. So,the possible values of r are 0,1,2,3,4,5 Set of positive odd integers are {1,3,5,7,9......}put a=1,3,5,7,9......a=bq+r1=6(0)+1=6q+1 [r=1]3=6(0)+3=6q+3 [r=3]5=6(0)+5=6q+5 [r=5]7=6(1)+1=6q+1 [r=1]9=6(1)+3=6q+3 [r=3] So,any positive integer is of the form 6q+1,6q+3,6q+5 where q is certain integer. tq |
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