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EXERCISE 1.21. Write whether every positive integer can be of the form 4q + 2, where q is aninteger. Justify your answer. |
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Answer» Let a be a given positive number.On dividing a by 4, let q be the quotient and r be the remainder.Then,by Euclid's algorithm,we have:a=4q+r where 0<=r<4a=4q+r where r=0,1,2,3a=4q+2=2(2q+1)It is clearly shown that 2q+1 is divisible by 2.Therefore,4q+2 is a positive integer. |
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