perplexus.info :: Numbers : Included in both A^B and B^A

Included in both A^B and B^A (Posted on 2023-06-01)

1) 'A' and 'B' are positive zeroless 2-digit integers which have one digit in common.
A 6-digit sequence, S, composed of only 3 unique digits, occurs in both A^B and B^A.
Find A, B, and S.

2) 'C' and 'D' are two other positive zeroless 2-digit integers which also have one digit in common.
A 6-digit sequence, T, composed of 6 unique digits, occurs in both C^D and D^C.
Find C, D, and T.

Neither S nor T has any leading zero.

Submitted by Larry

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Solution: (Hide)

A,B,S: 79, 94, 335375
79^94
238202645946674671901844030131688261840455609040130839498451613353756747499
045969428775114432599223684715089512540433018415983108109591226390930187505
73711401473264757112263998881
94^79
753529803906603364328062684879905074416038191684436076994112942137793353750
693678788439419755385754714791974652553974362629067333843924654151549669661
999104
C,D,T: 59, 89, 432061

59^89
403486525674138721277358818163343412346056820000557049137740680894095772750
769877883643206109427169312673615653196054182826495820074483198555479526164
53971739
89^59
103278611857003616688625589179443206140188442838630835763439139309446407559
32464940147984641594185920164994365747209

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	Subject	Author	Date
	computer solution	Charlie	2023-06-01 14:51:22

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