MathDB

Let

a_i,b_i

(i\equal{}1,2,...,n) be real numbers such that the

a_i

are distinct, and suppose that there is a real number

\alpha

such that the product (a_i\plus{}b_1)(a_i\plus{}b_2)...(a_i\plus{}b_n) is equal to

\alpha

for each

i

. Prove that there is a real number

\beta

such that (a_1\plus{}b_j)(a_2\plus{}b_j)...(a_n\plus{}b_j) is equal to

\beta

for each

j

Problem Statement