inside the rectangle such that each of the distances from 
such that![\[(a^2 + b^2 + c^2)^2 = 3(a^3b + b^3c + c^3a) + 1. \]](http://latex.artofproblemsolving.com/9/e/4/9e400fd807a9535ede983b75dcc307d8b75a35b6.png)
Y by
Let 
be the n-th prime number in increasing order for 
. Prove that there exists a sequence of distinct prime numbers 
satisfying 
for all 
be the n-th prime number in increasing order for 
. Prove that there exists a sequence of distinct prime numbers 
satisfying 
for all 
.
can't be represented as sum of 
primes.
and i have a solution using Dirichlet's theorem
.
and 
.
are distinct primes then 
and 
cannot both hold at the same time beacuse of odd even parity and 
is forced.
