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How do I find all pairs of (u, v) such that (3n+1)u + (2n+3)v = 7 ?
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Anonymous
2016-06-18 12:42:07 Post No. 142595
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Anonymous 2016-06-18 12:42:07 Post No. 142595 [Report]
How do I find all pairs of (u, v) such that (3n+1)u + (2n+3)v = 7 ?
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Anonymous 2016-06-18 13:48:31 Post No.142613
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Anonymous 2016-06-18 13:48:31 Post No.142613 [Report]
For any specified 'n' you can pick any 'u' and then solve the equation for 'v' in terms of 'u' and 'n'.
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Anonymous 2016-06-18 14:02:43 Post No.142615
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Anonymous 2016-06-18 14:02:43 Post No.142615 [Report]
>>142613
Anyone can do that; I need to find all pairs of (u, v) for which this holds true for all n, such that n is any arbitrary natural number.
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Anonymous 2016-06-18 14:23:39 Post No.142619
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Anonymous 2016-06-18 14:23:39 Post No.142619 [Report]
>>142615
If you want this to be true for every n, then the solution must be independent of n. So:
>3n*u+2n*v=0
>u+3v=7

Solving this system yields:
>u=-2
>v=3
>>
Anonymous 2016-06-18 15:14:22 Post No.142634
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Anonymous 2016-06-18 15:14:22 Post No.142634 [Report]
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>>142619
Thanks anon. Have a rare pepe.
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