I need to find all the $4$ digit numbers that the sum of every digit in the $4$th power is equal to the $4$ digit number. My first thought was brute forcing it but i was hinted that i can use tables for a faster method. Is there an algorithmic way using tables probably on doing that.
An example is $1634$ =$1^4$+$6^4$+$3^4$+$4^4$