## Evolving factoring efforts

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• One of my factoring schemes evolved into the following. z represents the integer to be factored. Let r1,r2,r3 be three primes selected so that (r1 + r2 + r3 +
Message 1 of 1 , May 4 7:52 AM
One of my factoring schemes evolved into the following.

z represents the integer to be factored.

Let r1,r2,r3 be three primes selected so that

(r1 + r2 + r3 + z) / 4 is an integer.

Consider the equation

( 4 f2 + r2) * ( 4 f3 + r3) = (4 f1 + r1) z

If we can solve this equation, we can expect that

< for some solutions > that

(4 f2 + r2) and (4 f3 + r3) have factors in common with z.

The equation

( 4 f2 + r2) * ( 4 f3 + r3) = (4 f1 + r1) z

Breaks into the six modulus equations

(4 f2 + r2) = 4 p1 f1 z mod r1
p1 ( 4 f3 + r3 ) = 4 f1 z mod r1

4 f2 = p2 (4 f1 + r1) z mod r2
p2 (4 f3 + r3) = (4 f1 + r1) z mod r2

(4 f2 + r2) = p3 (4 f1 + r1) z mod r3
4 p3 f3 = (4 f1 + r1) z mod r3

Hopefully, we might be able to solve these 6 modulus equations
for
p1,p2,p3,f1,f2,f3,

and then use them to determine values for the f1,f2,f3 in the equation

( 4 f2 + r2) * ( 4 f3 + r3) = (4 f1 + r1) z.

Kermit Rose

< kermit@... >
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