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March 8th, 2012, 09:47 PM   #1
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Find the largest value for which the system has a solution

For positive integer values of m and n find the largest value for which the system;




has a solution.
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March 9th, 2012, 05:27 AM   #2
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Re: Find the largest value for which the system has a soluti

Hello, sivela!

I have a start on this problem . . . Can anyone finish it?


Quote:
For positive integers and , find the largest values for which this system has a solution;

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[color=beige]. . . . . . [/color]

[color=beige]. . . . . . [/color]

[color=beige]. . . . . . [/color]

Now what?

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March 9th, 2012, 10:27 AM   #3
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Re: Find the largest value for which the system has a soluti

We have that

;

, which we observe is true if both and are 0.

Using this observation, we get the solution , from which



.

I wonder if there are other solutions...
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