If a function f satisfies f(~m+n)=f(~m)+f(n) for all m, n N and f(1)=1, then the largest natural number λ such that Σ k=1 ²⁰²² f(λ+k) ≤(2022)² is equal to _ _ _ _ _.

Sets, Relations and Functions: JEE Main 2024 Mathematics question

JEE Main 2024 · 9 Apr, Morning shift · Q35

JEE Main 20249 Apr, Morning shiftMathematicsMediumSets, Relations and Functions168× since 2002

If a function

f

satisfies

f(\mathrm{~m}+\mathrm{n})=f(\mathrm{~m})+f(\mathrm{n})

for all

\mathrm{m}, \mathrm{n} \in \mathbf{N}

and

f(1)=1

, then the largest natural number

\lambda

such that

\sum_\limits{\mathrm{k}=1}^{2022} f(\lambda+\mathrm{k}) \leq(2022)^2

is equal to _________.

Your answerType your answer. Integers and decimals are accepted.