MathDB

How many distinct triangles are there with prime side lengths and perimeter

100

?
Proposed by Muztaba Syed
Solution.

\boxed{0}

As the perimeter is even,

1

of the sides must be

2

. Thus, the other

2

sides are congruent by Triangle Inequality. Thus, for the perimeter to be

100

, both of the other sides must be

49

, but as

49

is obviously composite, the answer is thus

\boxed{0}

Problem Statement