Updated index.rst

index.rst

@@ -471,6 +471,7 @@ Integer Factorization and Discrete logarithm problem traditionally have been a m
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 	(*) Usual distance measures between histograms (Earth Mover Distance et al) apply as well to Quadratic forms represented by histograms similar to the one depicted earlier (or integer partitions) a sequitur from IntegerPartitions-Histogram-QuadraticForm bijection. 
+	(*) Chen's theorem - https://en.wikipedia.org/wiki/Chen%27s_theorem#:~:text=In%20number%20theory%2C%20Chen's%20theorem,the%20product%20of%20two%20primes) - states that every sufficiently large even number is either *) a sum of two primes or *) a sum of prime and semiprime - closer to proving Goldbach conjecture. Consequence of Chen's theorem which has implications for keypair creation and semiprime factorization: semiprime factorization could be written as difference of an even number and a prime.
 	(*) In Additive Number Theory, Fermat's Sum of Two Squares Theorem - https://en.wikipedia.org/wiki/Fermat%27s_theorem_on_sums_of_two_squares - states that Every odd prime p can be written as sum of two squares x^2 and y^2 if p = 1 (mod 4). Such primes are termed Pythagorean Primes. Previous Sum of Squares expansion is a generic case of Fermat's Theorem on Sum of Two Squares.
 	(*) By Fermat's Sum of Two Squares Theorem, Previous partition to Sum of Squares reduction solves a special case of Even Goldbach Conjecture if P = 1 (mod 4), Q = 1 (mod 4) and thus SOS(P) = a1^2 + b1^2 and SOS(Q) = a2^2 + b2^2 => N = 2n = xy = P + Q = SOS(P) + SOS(Q) = a1^2 + b1^2 + a2^2 + b2^2 which is Lagrange Sum of 4 squares.
 (*) Finding factor pair p and q of integer N=pq such that ratio p/q is closest to 1 is non-trivial problem of almost-square factorization of N (factor sides of rectangle of area N are almost equal - an integer equivalent of real square root algorithm). Such an almost-square is best suited for solutions to two ILPs (equated to factors) of square tile packing of rectangle of area N.