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March 16th, 2016, 01:43 PM   #1
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Exclamation Find the Smallest Positive Integer that...

Find the smallest positive integer which has a remainder of 2 when divided by 3, 5, or 7.

I know a tactic to find a positive integer that has a remainder of 2 when divided by 3, 5, or 7:

2 + (3×5×7) = 107.

However, 107 is not the smallest positive integer that meets this criteria. What's a good tactic that will allow you to find the smallest positive integer?

Last edited by skipjack; March 16th, 2016 at 01:48 PM.
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March 16th, 2016, 01:47 PM   #2
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Obviously, the smallest with the stated property is 2. Why add on 3×5×7 in the first place?
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March 16th, 2016, 02:07 PM   #3
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Sorry, I meant that it was greater than 2. I think that I forgot to specify that above.
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March 16th, 2016, 02:15 PM   #4
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3, 5 and 7 are coprime, so the smallest number that is divisible by 3, 5 and 7 is 105. Adding 2 to that gives 107, so the smallest possible number meeting the given requirements is 107.
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March 16th, 2016, 02:39 PM   #5
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Quote:
Originally Posted by John Travolski View Post
I think that I forgot to specify that above.
The question appears here (question 14) without such a specification.
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March 16th, 2016, 04:50 PM   #6
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How did you find that?
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March 16th, 2016, 05:23 PM   #7
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I used a Google search.
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