CMIMC 2022 Algebra and Number Theory Division 1 Problem 7

Let f(n) count the number of values 0 \leq k \leq n^{2} such that 43 \nmid\binom{n^{2}}{k}. Find the least positive value of n such that

43^{43} \left\lvert\, f\left(\frac{43^{n}-1}{42}\right)\right.