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A285176
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Elastic numbers: numbers n with two or more digits such that for any number m made by inserting any number of 0's between the digits of n, m is a multiple of n.
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4
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10, 15, 18, 20, 30, 40, 45, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700
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OFFSET
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1,1
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COMMENTS
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15, 18 and 45 are the only elastic numbers with no 0 as a digit. Proof: let n = 10*m+k, 0<k<10. Then n is elastic only if 90*m is a multiple of n, i.e., 90*m = n*q = (10*m+k)*q = 10*m*q + k*q. It follows that q<9, so k*q<100. But k*q = 10*m*(9-q) which is no less than 100 if n has at least 3 digits. Contradiction. - Andrey Zabolotskiy, Apr 18 2017
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REFERENCES
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D. Griller, Elastic Numbers, Rational Falcon, 2017, 45 & 95.
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LINKS
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EXAMPLE
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15 is an elastic number because 105, 1005, 10005, 100005, ... are all multiples of 15.
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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