Which of the following is true regarding Euler's Theorem on homogeneous functions as applied to production functions in economics?

A. The theorem requires the production function to be homogeneous of degree one.

B. It holds regardless of the degree of homogeneity of the production function.

C. The theorem requires that all inputs must exhibit constant returns to scale.

D. It only applies in scenarios where factor prices are equal to their marginal products.

E. It applies to all types of production functions without the need for homogeneity.

Choose the correct answer from the options given below: