English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let f(n){221n-2 if n=1 (2 + 22n-4)2n-4 if n&#x03F5; [2, 3, 4, 5] if n &#x03F5; [6, 7, 8 ....) We conjencturre that if a system T &#x2286; {xi +1 = xk, xi = xk: i, j, k &#x03F5; {l, ... ,n}} has only finitely many solutions in positive integers x1, ... , xn, then each such solution (x1, ... , xn) satisfies x1, ... , xn f(n). We prove that the function f cannot be decreased and the conjecture implies that there is an algorithm which takes as input a Diophantine equation, returns an integer, and this integer is greater than the heights of integer (non-negative integer, positive integer, rational) solutions, if the solution set is finite. We show that if the conjecture is true, then this can be partially confirmed by the execution of a brute-force algorithm.

A hypothetical way to compute an upper bound for the heights of solutions of a Diophantine equation with a finite number of solutions