# Can you subtract two integers using multiplication and division?

The multiplication operation is traditionally defined as "repeated addition", and division (with remainder) can be defined using repeated subtraction. Can we define subtraction the other way round? i.e., given two integers, can we calculate x-y using only operations of multiplication and division on x and y?

• To intepret the division as repeated soustraction is blatently wrong. – Martigan Jan 7 '15 at 12:15
• @Martigan: can you explain that statement ? – Yves Daoust Jan 7 '15 at 12:20
• "To intepret the division as repeated soustraction is blatently wrong"??? Looks like blatantly patronizing to me. Either explain what's wrong with it, or if you're unable to back it up, then simply refrain from making that kind of statement to begin with! And BTW, out of 10 words, you have about 3 blatant spelling errors in this single statement. – barak manos Jan 7 '15 at 12:26
• There are only two "natural" operations, adding and multiplying. In general (rings) they are not connected in the same way as they do in $\mathbb{Z}$. For example, multiplying a matrix by itself has "nothing" to do with adding of this matrix to itself. – Ofir Schnabel Jan 7 '15 at 12:29
• @Martigan: I wouldn't have made the 'spelling-errors' comment if the contents of your comment were constructive and informative by themselves. A simple search on Google would also tell you how to spell each word correctly, so this argument goes both ways, you know. Still, the point in answering questions here is to provide accurate reasoning, under the assumption that the person who has asked the question is already aware of the Google option. – barak manos Jan 7 '15 at 12:50