Let A A A be the largest positive integer that divides all the numbers of the form 3 k + 4 k + 5 k 3^k + 4^k + 5^k 3 k + 4 k + 5 k , and B B B be the ...

CAT Hard Divisibility Integer

Question

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:

Enter your answer as an integer value

divisibilitymodular arithmeticnumber theorycat 2022

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