Let-A-1-p-2-p-2-p-2-p-p-1-p-2-p-p-2-p-1-where-p-is-any-prime-number-Prove-that-for-any-value-of-p-however-we-split-this-set-into-two-disjunctive-sets-the-arithmetic-means-of-

Question Number 182203 by depressiveshrek last updated on 05/Dec/22

L e t A = {1^{p^{2} - p}, 2^{p^{2} - p}, \dots, {(p - 1)}^{p^{2} - p}, p^{2} - p + 1}

w h e r e p i s a n y p r i m e n u m b e r

P r o v e t h a t f o r a n y v a l u e o f p,

h o w e v e r w e s p l i t t h i s s e t i n t o t w o

d i s j u n c t i v e s e t s, t h e a r i t h m e t i c

m e a n s o f a l l e l e m e n t s o f b o t h s e t s

c a n n o t b e e q u a l t o e a c h o t h e r .