CAT 2022 Number System Question (Hard)

Question

Let be the largest positive integer that divides all the numbers of the form , and be the largest positive integer that divides all the numbers of the form , where is any positive integer. Then equals

Accepted Answer

Goal Find , where largest positive integer that divides all numbers of the form largest positive integer that divides all numbers of the form --- Step 1 Analyze A GCD of We want to ensure this expression is divisible by some constant for all . Let s check parity is odd for all is even is odd So Henc

CAT 2022

Quantitative

Number System

Hard

Let $A$ be the largest positive integer that divides all the numbers of the form $3^k+4^k+5^k$ , and $B$ be the largest positive integer that divides all the numbers of the form $4^k+3\left(4^k\right)+4^{k+2}$ , where $k$ is any positive integer. Then $(A+B)$ equals

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