Find smallest N for 5-and-21 sums
Company: Schonfeld
Role: Data Scientist
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Take-home Project
You are given two positive integers: 5 and 21. We say a positive integer `x` is **representable** if it can be written in the form
\[
x = 5a + 21b
\]
for some non‑negative integers `a` and `b` (i.e., using any number of 5s and 21s, order does not matter).
For example, 99 is representable because:
- 99 = 21 + 21 + 21 + 21 + 5 + 5 + 5.
Find the **smallest integer N** such that **every integer greater than or equal to N** is representable.
Output this minimal value of `N`.
Quick Answer: This question evaluates understanding of integer linear combinations and elementary number theory, framed as a Frobenius coin problem that examines representability using non-negative multiples of 5 and 21.