3 variable diophantine system
Number Theory
Level
4
Given the positive integers \(a \le b \le c \le 100 \) satisfy the system of equations below.
\[ \begin{cases} {a+b=c} \\ {a^4+b^2=c^2} \\ {a^3=b+c} \\ \end{cases} \]
Find the sum of all possible values of \(a+b+c\).
by
Vincent Huang