Question

what is the suitable condition for R in the division algorithm a=bq+r


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Answer 1

Given two integers a and b, with b ≠ 0, there exist unique integers q and r such that

a = bq + r

and

0 ≤ r < |b|,

where |b| denotes the absolute value of b.

In the above theorem, each of the four integers has a name of its own: a is called the dividend, b is called the divisor, q is called the quotient and r is called the remainder.

Division is not defined in the case where b = 0.