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Three Power and Product Divisibility (Posted on 2015-09-19) Difficulty: 3 of 5
Find all pairs (X,Y) of positive integers such that each of 3X + 1 and 3Y + 1 is divisible by X*Y.
Prove that there are no others.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts 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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