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February 2nd, 2014, 03:41 AM   #1
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for N

solve in N natural number
x^3-y^3-xy=61
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February 2nd, 2014, 04:03 AM   #2
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Re: for N

I found two solutions:

x = -5, y = -6 (but negative numbers)
x = 6, y = 5

But I'm not sure if there are other solutions.
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February 2nd, 2014, 10:22 AM   #3
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Re: for N

I guess not, (x, y) = (5, 6) is the only solution s.t. 1 <= x, y <= 6.
For y > x > 5 (and x, y in N), y^3 - x^3 - x*y > 61, for x > y > 5, y^3 - x^3 - x*y < 61.
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February 2nd, 2014, 10:39 AM   #4
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Re: for N

Nevermind.
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