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Find two numbers a,b such us: a+b=5432 & LCM[a,b]=223020

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  • Subject: [mg122153] Find two numbers a,b such us: a+b=5432 & LCM[a,b]=223020
  • From: dimitris <dimmechan at yahoo.com>
  • Date: Sun, 16 Oct 2011 16:45:09 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

This is taken from the recent book (2010): " Mathematica: A Problem-
Centered Approach" by R. Hazrat.

"The sum of two positive integers is 5432 and their least common
multiple is
223020. Find the numbers."

A solution:

Do[If[LCM[i, 5432 - i] == 223020, Print[i, "  ", 5432 - i]], {i, 1,
2718}]
1652  3780

I wonder if we can solve the system of equations:

a+b==5432&&LCM[a,b]==223020

using codes that contain built in functions like Reduce.

I guess this is not a trivial one because the so much powerful Reduce
itself fails

In[1]:= Reduce[{a + b == 5432, LCM[a, b] == 223020}, {a, b}, Integers]

During evaluation of In[1]:= Reduce::nsmet:This system cannot be
solved with the methods available to Reduce. >>

Out[1]= Reduce[{a + b == 5432, LCM[a, b] == 223020}, {a, b}, Integers]

Any ideas?

Dimitris



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