Almost all even positive integers can be represented by the sum of two regular primes. Also one must find the Goldbach Parttion of each even integer as one may think that an even integer is not the sum of two regular primes. It would be appreciated if someone could find a even number that isn’t …
Continue reading “A variant on the Goldbach Conjecture. Conjecture no.15”
What is the lower bound for the number of pairwise coprime cubes that can sum to any positive integer. As always I welcome the readers to try and solve this problem. Nunghead
The equation n!!+1=k^2n+1 where n>0 has no integer solutions for all positive integers. Here the double factorial indicates that the product of all even or odd integers =< n. For example 8!! is equal to 2*4*6*8. As always I welcome the readers to try proving or disproving this conjecture. https://en.m.wikipedia.org/wiki/Brocard%27s_problem
Is there a convex shape in any dimension greater than three that has lower packing density than the hypersphere in hyperbolic space. This question is motivated by Ulam’s Packing conjecture. As always I welcome the readers to prove or disprove this problem. Nunghead
For any countable comunitive ring is Hilbert’s Tenth problem undecidable and if undecidable is there a minimum set of variables such that the problem is decidable. As always I welcome the readers to prove or disprove this problem. https://en.m.wikipedia.org/wiki/Hilbert’s_tenth_problem Nunghead
The generalized Fermat Catalan Conjecture is the statement that the equation: Does the equation a1^k1+a2^k2+a3^k3… +a^k =b^c has finitely many or no solutions where a1, a2, a3, … are all relatively prime and that 1/k1 +1/k2+ 1/k3… < 1. As always I welcome my readers to prove or disprove this conjecture. I would like some …
Continue reading “Conjecture no. 11 The generalized Fermat Catalan Conjecture”
The equation P, P+2x=Ap +B where all constants are positive integers and all x values are also positive integers,the GCD of (a,b)=1 , b-a if b>a or a-b if a>b /= 2x so that when a prime is prime for both P, P+2x and where x is an even number or odd there also exists …
Continue reading “Conjecture no. 8 – Another conjecture relating to the Sophie Germain Primes”
There exists infinitely many primes where x is a prime, and ax^n +c is prime for all positive integers, where also all coefficients are positive integers, whose degrees are also all positive integers, wherence the polynomial must also not be factorable over the positive integers, and the GCD of (a,c) must equal one and whose …
Continue reading “Generalized conjecture on the Sophie Germain Primes, Conjecture no.7”
I will start by explaining what a transcendental number is and I will also give a short survey article to explain the history of transcendental numbers. A transcendental number is a number that is not the solution of a polynomial with rational coefficients as opposed to the numbers that are the solutions or roots of …
Continue reading “Conjecture no. 6 – On transcendental numbers”
There is at least one prime in the interval n^a to (n+1)^b, given that,i) n, a, b are positive integers greater than 1 and cannot have the same value.ii) a and b are relatively prime; i.e., GCD of (a,b) =1… at least 1 prime exists in this interval. However, if a and b are not …
My Mathematics work and other extraneous diversions