perplexus.info :: Just Math : Three Power and Product Divisibility

Three Power and Product Divisibility (Posted on 2015-09-19)

Find all pairs (X,Y) of positive integers such that each of 3^X + 1 and 3^Y + 1 is divisible by X*Y.
Prove that there are no others.

No Solution Yet Submitted by K Sengupta

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re: computer exploration

Comment 2 of 2 |

(In reply to computer exploration by Charlie)

UBASIC program

10 for Tot=1 to 2000

20 for X=1 to int(Tot/2)

30 Y=Tot-X

40 V1=3^X+1

50 V2=3^Y+1

60 D=X*Y

70 R1=V1@D:R2=V2@D

80 if R1=0 and R2=0 then print X;Y,V1;V2,D

90 next

100 next

still finds only the two solutions (1,1) and (1,2) -- and also of course (2,1) is to be counted as well.

Posted by Charlie on 2015-09-20 18:58:36

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