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# help Number Theory

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Suppose that x,y,z are positive integers satisfying x is less than or equal to y is less than or equal to z, and such that the product of all three numbers is three times their sum. What is the sum of all possible values of z?

Sep 23, 2021

#1
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159  167  235  333  Total =  4

9  +  7  +  5  +  3==24 sum of "z's"

Sep 23, 2021
#2
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How did you get that guest?

Melody  Sep 23, 2021
#3
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By a very short computer code in C++.

Guest Sep 23, 2021
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Is the answer supposed to make any sense?  ... Edit:  Catmeg has explained and I will take a look with fresh eyes.

When you use C++ or any other non-obvious aid to answer questions could you please state that you have done so.

It will cut down on confusion. Melody  Sep 24, 2021
edited by Melody  Sep 24, 2021
edited by Melody  Sep 24, 2021
#5
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I think what guest means by 159 is that

x = 1

y = 5

z = 9

3(1+5+9) = 1*5*9

=^._.^=

Sep 24, 2021
#6
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Thanks Catmg

I will have to look at the question/answer harder.

Melody  Sep 24, 2021