$Suppose$ \;a, b\; $and$ \;c \;$are integers. We have,$
a^3+b^3
$We examine$\;a^3\;$and we notice that,$
a^3 \equiv 0\; ($modulo$\; 7)
a^3 \equiv 1\; ($modulo$\; 7)
a^3 \equiv 6 \;($modulo$\; 7)
$This means, by addition in modular arithmetic,$
a^3+b^3 \equiv 0 \;($modulo$\; 7)
a^3+b^3...