Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have question on behavior of floor division. if i have,

-7/3 = -3 and remainder = 2
also -7/3 = -4 remainder = 5   

it can have many results. When we make tally all are correct.Then what is the use of floor division is not stick to one solution as truncated division.
Where floor division can be applied any example.

share|improve this question
2  
It means $5\equiv 2\pmod 3$... in this case, we pick the least positive remainder. –  J. M. Jul 22 '12 at 9:40
add comment

1 Answer

up vote 1 down vote accepted

The Division Theorem says that if $a$ and $b$ are integers, $b\ne0$, then there are unique integers $q$ and $r$ such that $$a=bq+r,\quad0\le r\lt|b|$$ So there is only one result, with that condition on the remainder, $r$.

The Division Theorem is the first step in the most frequently seen proof of the Unique Factorization Theorem. Generalizations of the Division Theorem can be used to prove uniqueness of factorization in many other settings, for example, unique factorization of polynomials with real coefficients.

share|improve this answer
    
Thanks Gerry Myerson. –  sandip karanjekar Jul 22 '12 at 9:59
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.