Problems

 

 

48.6 What is the smallest area of a triangle in the coordinate plane whose vertices have integer coefficients?

 

48.10 Let a, b, c be positive integers such that a^2 + b^2 = c^2. Prove that, for all positive integers n,

a^{2n+1} + b^{2n+1} + c^{2n+1}     and     (b + c)(c + a)(a + b)

are divisible by a + b + c.