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Week #6 Solution Fall 2008
Check all of your multiplication facts, do a few division
problems, and then get set for the WSU Mathematics Department’s
DON’T TEST
EVERY
NUMBER!!
There are three numbers less than 10,000 with the property that on
division by 10, 9, 8, 7, 6, 5, 4, 3, and 2 the remainder left is always
one less than the number divided by. Can you find them?
Solution. Any number which is 1 less than a number which has 2, 3, 4, 5,
6, 7, 8, 9, and 10 as factors will have the required property. The smallest
such number will thus be 1 less the LCM {2, 3, 4, 5, 6, 7, 8, 9 10} = 2520.
Further, any number of the form (2520n -1) will have the same property. In
particular the three less than 10,000 are 2,519, 5,039 and 7,559.
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