The smallest positive integer divisible by $2004$ and writing in base ten with the only digits $2$ and $4$ is $222 444$. What is the next? And the next of the next?
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Ok thanks, it is a problem to attack with congruences and modulo,but it don't know how... – Marcus15 Mar 22 '17 at 13:49
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Are you looking for the smallest or all of them? – Mar 22 '17 at 13:51
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1It most definitely isn't the only one. $222444222444$ is another one, and so is $222444222444222444$, etcetera – Mar 22 '17 at 13:53
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the first number is 42244442244 but I don't know how to find it. – Marcus15 Mar 22 '17 at 13:54
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The one after that is $44244424224$, and the one after that is $222444222444$ – Mar 22 '17 at 13:54
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Ok but how I can find them? – Marcus15 Mar 22 '17 at 13:56
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The problem asks the first that is next of 222444 and the next of the next. – Marcus15 Mar 22 '17 at 14:00