Prove that the equation
Proof:
Solution by Andrei Stefanescu
For any 
Note that the triplet 
Since we can define this triplet for all k’s, there will be an infinity of solutions.
QED.
More later,
Nalin Pithwa
Prove that the equation
Proof:
Solution by Andrei Stefanescu
For any
Note that the triplet
Since we can define this triplet for all k’s, there will be an infinity of solutions.
QED.
More later,
Nalin Pithwa
Parametric form of solution is most dangerous one, since it asks you to explain “how you thought of this parametric form?”.
I would be like to know the thinking involved behind selection of this parametric form.
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There are questions in Math which have been or can be solved by a stroke of imagination. The proposed solution is one such. May I know whether you can think of any other approach ? Kindly share with us. – Nalin
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I can assure you that no magic is involved here. I failed to find the logical path of thoughts leading to this solution, that’s why I asked you for it. I would suggest you to think over it, till you are able to find the logical path of thoughts. See, section 1.3 in this file: https://gaurish4math.files.wordpress.com/2015/12/diophantine-equations-gaurish-rev4.pdf
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thanks…will certainly try and keep you posted 🙂
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In words of G. H. Hardy:
“A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.”
A Mathematician’s Apology (London 1941).
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Thanks for a quotation from my all-time favourite mathematician
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