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For how many ordered pairs (A,B) where A and B are positive integers is $AAA_7 + BBB_7 = 444_7$?

 Dec 9, 2021
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Converting everything to base 10:

49A + 7A + A = 57A

57A + 57B = 228.

This means that A+B=4. Since A and B are positive integers:

(1,3)

(2,2)

(3,1)

 Dec 10, 2021

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