How do I find all pairs of (u, v) such that (3n+1)u + (2n+3)v = 7 ?
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How do I find all pairs of (u, v) such that (3n+1)u + (2n+3)v = 7 ?
For any specified 'n' you can pick any 'u' and then solve the equation for 'v' in terms of 'u' and 'n'.
>>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.
>>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
>>142619
Thanks anon. Have a rare pepe.