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Simple Division

Unreviewed import — a classic from the public domain; its solution has not been machine-checked yet.

math
Sometimes a very simple question in elementary arithmetic will cause a good deal of perplexity. For example, I want to divide the four numbers, 701, 1,059, 1,417, and 2,312, by the largest number possible that will leave the same remainder in every case. How am I to set to work Of course, by a laborious system of trial one can in time discover the answer, but there is quite a simple method of doing it if you can only find it.

Solution

Commit an attempt to unseal the proof. Write your answer — right or wrong, thinking it through is the point.

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