Hint:
(3n+1)^2+4n^3=m^2
- Phlembac Adib Hasan
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Prove that there exist infinitely many positive integer $n$s such that $(3n+1)^2+4n^3$ is a perfect square.
Hint:
Hint:
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Re: (3n+1)^2+4n^3=m^2
For all $k\in\mathbb N$ we have $n=k^2+k\Rightarrow (3n+1)^2+4n^3=(2k+1)^2(k^2+k+1)^2$.
- What is the value of the contour integral around Western Europe?
- Zero.
- Why?
- Because all the poles are in Eastern Europe.
Revive the IMO marathon.
- Zero.
- Why?
- Because all the poles are in Eastern Europe.
Revive the IMO marathon.
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Re: (3n+1)^2+4n^3=m^2
how should i think to solve this question? i.e the problem deals with which topic of math?
- Phlembac Adib Hasan
- Posts:1016
- Joined:Tue Nov 22, 2011 7:49 pm
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Re: (3n+1)^2+4n^3=m^2
Typically these equations are called Diophantine Equations. And it's part of Number Theory. I don't know if there is any good (olympiad level) material on this topic. Try "Introduction to Diophantine Equations", perhaps?
Also, in this thread, you are not required to solve that equation. It was actually an interesting factorization (that saved my life) while working on some other sh*ts.
Also, in this thread, you are not required to solve that equation. It was actually an interesting factorization (that saved my life) while working on some other sh*ts.
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