Question 1025739
<pre>
Sorry, there aren't any 3 such consecutive positive integers.
Here is why there cannot be:

5²+6²+7² = 25+36+49 = 110
6²+7²+8² = 36+49+64 = 149
7²+8²+9² = 49+64+81 = 194
8²+9²+10² = 64+81+100 = 245

See?  The sums of squares skip
right over 154.  There is no solution.

Edwin</pre>