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 As low as possible (Posted on 2013-04-12)
What is the lowest value of a product of two positive numbers a and b, given that a+b=a*b?

 No Solution Yet Submitted by Ady TZIDON No Rating

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 Another Computer Analysis Comment 6 of 6 |
I sought to see how a and b might appear if seen as fractions.
In the following program a = j/k and b = l/m.

A print-out (poorly formatted) from the listing appears below; 4 appears as the lowest product.

OPEN "c:\qb64\work\sum_prod.txt" FOR OUTPUT AS #1

FOR j = .1 TO 10 STEP .1
FOR k = .1 TO 10 STEP .1
FOR l = .1 TO 10 STEP .1
FOR m = .1 TO 10 STEP .1
IF (j / k + l / m) = (j / k) * (l / m) THEN
PRINT j; k; l; m, (j / k) * (l / m)
PRINT #1, j; k; l; m, (j / k) * (l / m)
END IF
NEXT: NEXT: NEXT: NEXT
CLOSE 1

.2  .1  .2  .1              4
.2  .1  .4  .2              4
.2  .1  .6  .3              4
.2  .1  2  1                4
.2  .1  8.599997  4.299998  4
.4  .2  .2  .1              4
.4  .2  .4  .2              4
.4  .2  .6  .3              4
.4  .2  2  1                4
.4  .2  8.599997  4.299998  4
.6  .3  .2  .1              4
.6  .3  .4  .2              4
.6  .3  .6  .3              4
.6  .3  2  1                4
.6  .3  8.599997  4.299998  4
1  .3  2  1.4               4.761905
2  .5  2  1.5               5.333334
2  .6  2  1.4               4.761905
2  .7  2  1.3               4.395605
2  .8000001  2  1.2         4.166667
2  .9000001  2  1.1         4.040404
2  1  .2  .1                4
2  1  .4  .2                4
2  1  .6  .3                4
2  1  2  1                  4
2  1  8.599997  4.299998    4
2  1.1  2  .9000001         4.040404
2  1.2  2  .8000001         4.166667
2  1.3  2  .7               4.395605
2  1.4  1  .3               4.761905
2  1.4  2  .6               4.761905
2  1.5  2  .5               5.333334
8.199995  .5  8.199995  7.699995          17.46493
8.199995  7.699995  8.199995  .5          17.46493
8.399996  1.3  8.399996  7.099996         7.644633
8.399996  7.099996  8.399996  1.3         7.644633
8.499996  1.7  8.499996  6.799996         6.249997
8.499996  6.799996  8.499996  1.7         6.249997
8.599997  4.099998  8.599997  4.499998    4.008672
8.599997  4.199998  8.599997  4.399998    4.002164
8.599997  4.299998  .2  .1  4
8.599997  4.299998  .4  .2  4
8.599997  4.299998  .6  .3  4
8.599997  4.299998  2  1    4
8.599997  4.299998  8.599997  4.299998    4
8.599997  4.399998  8.599997  4.199998    4.002164
8.599997  4.499998  8.599997  4.099998    4.008672

 Posted by brianjn on 2013-04-12 22:49:45

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