Divide and Rule
Number Theory
Level
3
Once I performed a series of divisions where I got that the dividend is equal to remainder. Are my divisions flawed?
Note: I perform divisions for non-negative integers.
This problem is original.
Some may be flawed.
Definitely flawed.
Not flawed at all.
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If we let D as the dividend , d as the divisor , q as the quotient and r as the remainder , By division algorithm we have:
D = d q + r
But since D = r , we cancel them from both the sides to get d q = 0 .
Case 1: When d = 0 , my division is definitely flawed because I cannot divide a number by 0 .
Case 2: When q = 0 , implies that the dividend itself is 0 that is D = 0 , which is possible.
Hence , some of my divisions might be flawed,.