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# Problem 582

## Nearly isosceles 120 degree triangles

Let a, b and c be the sides of an integer sided triangle with one angle of 120 degrees, a≤b≤c and b-a≤100.
Let T($n$) be the number of such triangles with c≤$n$.
T(1000)=235 and T(108)=1245.
Find T(10100).