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0 $begingroup$ I tried to think about some characteristics of the trees, for example, they have a number of edges equal to $|text{Vertices}|-1$ and of course the handshaking lemma but I couldn't find properly logical reasoning. Any help? discrete-mathematics graph-theory trees share | cite | improve this question edited Dec 24 '18 at 18:01 EdOverflow 251 1 9 asked Dec 24 '18 at 17:44 PCNF PCNF 133 8 ...

2 $begingroup$ I'm concerning myself with factoring semi-primes and believe that if given a large semi-prime ( $N$ ) one finds a non-trivial sum of squares representation: $$ x^2 + y^2 = N$$ Then one can efficiently retrieve a factorization of $N$ . My intuition for this belief is that I think the "factoring" problem over the gaussian integers is difficult and note that such a representation can be in linear time converted into a factorization $(x + yi) ( x- yi)$ when considering gaussian integers. But it's not clear to me how to leverage this information for regular integers. More Notes: So I realized after @Jack D'Aruzio's comment that this information could be exploited by computing $i$ mod $N$ That is finding some constant $c$ such that $c^2 = -1 mod N$ . Then we have...

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