Problems & Puzzles: Puzzles
Puzzle 154. Extension and Variation of the GC
Burrage, poses in one of his Web pages
an "Extensión of the Goldbach's Conjecture" (EGC). This
EGC proposes that:
He also wonders if this his conjecture can be proved true supposing true the Goldbach Conjecture (GC).
is a kind of easy to prove that the EGC follows directly from the GC, but I
will let the readers to find that proof his own way. I
will only provide - as indirect evidence that such proof exists - a code
in Ubasic of mine to produce such representations for A & B >3.
Some examples are:
I propose a variation of the Burrage's EGC that I will name VEGC:
Does the VEGC follow also from the GC?
What is that X condition?
c) Can you produce a code to make such expansion?
Luis Rodríguez has proved his own way the Burrage's conjecture (EGC):
As you can see this correct proof provides another solution than the given by my code written above, specifically to the case where N is odd. In the Rodríguez solution for N=5x7 then A=5 and N=(35-2(5-3)-3)+2(5-3)+3=(28)+(2+2+3)=(11+17)+(2+2+3)
While using my code the solution is: