CAT 2023 Number System Question (Hard)

Question

Let , , , and be natural numbers such that , , and , ten the largest possible value of is

Accepted Answer

Step 1 Factorize the RHS So Step 2 To maximize , minimize and maximize . Let Let Then Now reverse the assignment Let , so Let , so Then Try pushing more powers into Let Then , Now, Final Answer The largest possible value of is 579

CAT 2023

Quantitative

Number System

Hard

Let $a$ , $b$ , $m$ , and $n$ be natural numbers such that $a > 1$ , $b > 1$ , and $a^m \cdot b^n = 144^{145}$ , ten the largest possible value of $n - m$ is

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