Question 1207720
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The numbers are 2 more than a multiple of either 5, 6, or 7.<br>
Since 5, 6, and 7 have no common factors, the numbers have to be 2 more than a multiple of 5*6*7=210.<br>
The numbers N satisfying that requirement in the interval [0,1000] are 2, 212, 422, 632, and 842.<br>
ANSWER: 5 solutions<br>