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- Thread starter jmich79
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HallsofIvy

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Saying "F1= (.7373) base n" means F1= 7/n+ 3/n^{2}+ 7/n^{3}+ 3/n^{4}. Similarly, saying "F1= (.5252) base m" means that F1= 5/m+ 2/m^{2}+ 5/m^{3}+ 2/m^{4}. Putting those together you know that 7/n+ 3/n^{2}+ 7/n^{3}+ 3/n^{4}= 5/m+ 2/m^{2}+ 5/m^{3}+ 2/m^{4}. Likewise, F2= (.3737) base n and F2= (.2525) base m gives 3/n+ 7/n^{2}+ 3/n^{3}+ 7/n^{4}= 2/m+ 5/m^{2}+ 2/m^{3}+ 5/m^{4}. That gives you two equations to solve for the two unknown numbers m and n.

Edited to replace "y/n^{3}" by "7/n^{3}". My finger slipped!

Edited to replace "y/n

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I tried doing this method without the y variable and was not able to solve for it. I came up with some crazy nubers. Can you please explain further?

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dOES ANYONE KNOW HOW TO SOLVE THIS EQUATION SIMULTANEOUSLY?

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It seems to me that you're supposed to spot the weird symmetry in the numbers here. '7373', '3737', '5252', '2525'. HallsofIvy outlines a general method of solving this problem when the given numbers have no special pattern, but f:grumpy:k only knows how you'd solve those simultaneous equations!

My thoughts. Try adding F1 and F2 in base m and in base n. Assume, just to make it easier, that n>10 and m>7 (if that's not the case I'm sure it'll turn up in some contradiction or other)

(eta: well, I'm not making much progress... but I still think that it's important to note the symmetry here. It means something, I'm sure of it.)

My thoughts. Try adding F1 and F2 in base m and in base n. Assume, just to make it easier, that n>10 and m>7 (if that's not the case I'm sure it'll turn up in some contradiction or other)

(eta: well, I'm not making much progress... but I still think that it's important to note the symmetry here. It means something, I'm sure of it.)

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