If a and b are two integers $b > 0,$ then there exist two integers q and r such that

b = a q + r,

where

0 < r < b

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b = r q + a,

where

0 < r < b

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a = b q + r,

where

0 < r < b

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a = b r + q,

where

0 < r < b

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Solution

The correct option is C $a = b q + r,$ where $0 < r < b$
$L e t a a n d b a r e i n t e g e r s, b > 0 L e t u s c o n s i d e r t h e A . P w i t h f i r s t t e r m a a n d c o m m o n d i f f e r e n c e b . T h e n t h e s e r i e s i s - - - - -, (a - 3 b), (a - 2 b), (a - b), a, (a + b), (a + 2 b), - - - - L e t r b e t h e s m a l l e s t t e r m s a t i s f y i n g t h e i n e q u a l i t y 0 < r < b . T h e n w e c a n h a v e a n o n i n t e g e r q s u c h t h a t a - b q = r \Rightarrow a = b q + r - - - - 0 < r < b ∴ O p t i o n C i s c o r r e c t .$

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Similar questions

According to Euclid's division lemma, if $a$ and $b$ are two positive integers with $a > b,$ then which of the following is true? (Here, $q$ and $r$ are unique integers.)

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If a and b are two integers b>0, then there exist two integers q and r such that

If a and b are two integers $b > 0,$ then there exist two integers q and r such that