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Geometric Sequence Settlement (Posted on 2013-08-07) Difficulty: 3 of 5
Determine the total number of ways in which 111 can be written as a sum of three distinct nonzero integers which are in geometric sequence.

Prove that there are no others.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts computer partial solution | Comment 1 of 4

The program checks for all possible sets of three distinct positive integers. Cases of negative, positive, negative or positive, negative, positive have not been considered here:

FOR a = 1 TO 111 / 3
FOR b = a + 1 TO (111 - a) / 2
c = 111 - a - b
IF c > b THEN
    IF a * c = b * b THEN PRINT a; b; c: ct = ct + 1
END IF
NEXT
NEXT

PRINT ct

It finds 2 solutions in which all the integers are positive:

1  10  100
27  36  48


  Posted by Charlie on 2013-08-07 12:28:09
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