What is the value of $a + b + c + d$ if the following equation holds?

Question

If $a, b, c$ and $d$ are positive integers less than $7$ and $$a(7)^3 + b(7)^2 + c(7) + d = 901$$ What is the value of $a + b + c + d$?

Is it related to consum of roots and product of roots?

Answer 1

HINT:

Clearly, the Left hand Side represents a number in base $7$

Reference : Base Conversion

So, $\displaystyle a=\lfloor901/{7^3}\rfloor$