Before we start, let us define two functions, let \(n\) a positive integer and \(m\) is the number of total prime divisors of \(n\) (for example, if \(n=12\) then \(m=|\{2,2,3\}|=3\), and we define \(\lambda(n)=(-1)^m\). And also : \[L(n)=\sum_{k=1}^{n} \lambda(k)\] Polya conjectured that \(L(n)\leq 0\) for any \(n\geq 2\), but this was disproved fifty years ago and the counter example was a very large number (almost a billion).

**Our task :** let us assume that we do not know that there is a counter-example and we try to find one, what do you suggest as the best programming language for this ? and how can we speed up the search for a counter example ?

Please share your codes and running time and the machine specifications and remember that they made it work on a 1958 computer, it should be doable on a 2014 computer.

Wiki page :Polya's conjecture.

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TopNewestVous n'êtes pas mauvais en maths, êtes-vous? Je voudrais avoir le temps de travailler sur ce plus mais je n'ai pas. Il est très intéressant! – Finn Hulse · 2 years, 10 months ago

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Anyway, thanks for replying. And for your question : I'm not good too. – Haroun Meghaichi · 2 years, 10 months ago

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