a) Show that there are five integers $A, B, C, D$, and $E$ such that $2018 = A^5 + B^5 + C^5 + D^5 + E^5$ b) Show that there are no four integers $A, B, C$ and $D$ such that $2018 = A^5 + B^5 + C^5 + D^5$
Source: Lusophon 2019 CPLP P5
Tags: number theory, Sum of powers
a) Show that there are five integers $A, B, C, D$, and $E$ such that $2018 = A^5 + B^5 + C^5 + D^5 + E^5$ b) Show that there are no four integers $A, B, C$ and $D$ such that $2018 = A^5 + B^5 + C^5 + D^5$