Given the set of natural numbers, {1, 2, 3, 4,…}, find the 2010th number in this set that is not divisible by 2 or 3.
Let be the set of natural numbers not divisible by 2 or 3.
Then all must be congruent to either 1 or 5, modulo 6.
Hence the 2010th smallest member of must be .
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Let
be the set of natural numbers not divisible by 2 or 3.
Then all
must be congruent to either 1 or 5, modulo 6.
Hence the 2010th smallest member of
must be 
.