Interexchangeable quotients and divisors?

Number Theory Level 3

Can we find distinct positive integers $a$ and $b$ such that

when $a$ is divided by $b$ , it gives a remainder of $c$ , and
when $b$ is divided by $a$ , it gives a remainder of $c$ as well?

Yes No

1 solution

X X
Jul 1, 2018

Let $a<b$ ,then when $a$ is divided by $b$ ,the remainder is $a=c$ .When $b$ is divided by $a$ ,then the remainder is $a$ .But the remainder should be smaller than the divisor,so the remainder shouldn't be $a$ .Hence,the answer is no .

Interexchangeable quotients and divisors?

1 solution

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