A question of remainders

Right, now for a problem that is well within the scope of those of you with micros, or even programmable calculators.

If you divided 2519 by 10, there is a remainder of 9.
If you divide 2519 by 9, there is a remainder of 8.
If you divide 2519 by 8, there is a remainder of 7, and so on.
Can you find two other numbers with the same property?

A simple computer solution, with a loop from 5,000 to 50,000, and several remainder tests within that loop. The process can be considerably speeded up if you make the increment within the loop equal to the largest of the divisors – in this case 17. The rest is easy, and the answer that you should get is 29031.


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