write whether every positive integer can be of the form 4q+2 where q is an integer justify your answer.
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Answer:
On dividing a by 4, let q be the quotient and r be the remainder. It is clearly shown that 2q+1 is divisible by 2. Therefore,4q+2 is a positive intege
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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<4
a=4q+r where r=0,1,2,3
a=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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