20181205, 02:59  #1 
Nov 2016
8DB_{16} Posts 
Schinzel's hypothesis H
For any polynomial f(x) in one variable with positive degree and integer coefficients:
f(x) = a_nx^n+a_{n1)x^{n1}+a_{n2)x^{n2}+...+a_2x^2+a_1x+a_0 with n>=1 Like The Sierpinski/Riesellike problem, if the values of the polynomial f(x) have a single trivial factor for all xvalues, then we take out this factor (e.g. x^2+x+2 become {1/2*x^2+1/2*x+1}, since all values of this polynomial are divisible by 2), besides, if f(x) is not irreducible over the integers, then we must factorize f(x) (e.g. x^21 become {x1,x+1}, since x^21=(x1)*(x+1)). Here are some examples: Code:
f(x) the polynomials x^4 {x,x,x,x} x^2+1 {x^2+1} x^21 {x1,x+1} x^3+1 {x+1,x^2x+1} x^4+1 {x^4+1} x^41 {x1,x+1,x^2+1} x^2+x {1/2*x,x+1} for even x, {x,1/2*x+1/2} for odd x x^2+x+2 {1/2*x^2+1/2*x+1} x^2x1 {x^2x1} x^2x6 {x3,1/2*x+1} for even x, {1/2*x3/2,x+2} for odd x x^3+2*x+9 {1/3*x^3+2/3*x+3} x^5+x+1 {x^2+x+1,x^3x^2+1} Note: We also consider the negative primes (e.g. 2, 3, 5, 7, 11, ...) as primes, since they are primes in the ring Z. Last fiddled with by sweety439 on 20181205 at 03:33 
20181205, 03:07  #2 
Nov 2016
2,267 Posts 
We take the corresponding from positive integers to integervalues polynomials:
if N=2^{a_0}*3^{a_1}*5^{a_2}*7^{a_3}*11^{a_4}*... then we take b_k=A001057(a_k) for all k and set the corresponding polynomial of N is b_0+b_1x+b_2x^2+b_3x^3+b_4x^4+... Last fiddled with by sweety439 on 20181205 at 03:07 
20181205, 03:26  #3  
Nov 2016
4333_{8} Posts 
Quote:
twin prime conjecture: x^21 the fourth of Landau's problems: x^2+1 infinitude of prime quadruplets: x^410*x^2+9 infinitude of Sophie Germain primes: 2*x^2+x 

20181205, 03:27  #4  
Nov 2016
2,267 Posts 
Quote:
Last fiddled with by sweety439 on 20181205 at 03:30 

20181205, 05:28  #5 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
9,127 Posts 
I don't think you are quoting yourself elegantly enough.
When writing four posts in a row  it is imperative that the 2nd post quotes post #1 entirely, post #3 quotes both post #1 and post #2 in their entirety, and the 4th one  well, I hope you get the idea. Only then your messages will start getting to their audience. 
20181205, 15:25  #6  
Nov 2016
2,267 Posts 
Quote:


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