MathDB

Let

p

be a prime number and let further

p + 1

rational numbers

a_0,...,a_p

with the following property given: If one removes any of the

p + 1

numbers, then the remaining may be split in at least two groups , which all have the same mean value (for different distant numbers, however, these mean values may be different). Prove that all

p + 1

numbers are equal.

Problem Statement