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Let p, c be distinct odd primes, and l \ge 2 an integer. We find sufficient conditions for the Diophantine equation cy^l=(x^p-1)/(x-1) not to have integer solutions.
A subset of {1,2,3,...}^n whose non-computability leads to the existence of a Diophantine equation whose solvability is logically undecidable
Hilbert’s Tenth Problem logically undecidable Diophantine equation Logic
2011/9/22
Abstract: Let B(n)={(x_1,...,x_n) \in {1,2,3,...}^n: for each positive integers y_1,...,y_n the conjunction
(\forall i,j,k \in {1,...,n} (x_i+x_j=x_k ==> y_i+y_j=y_k)) AND
\forall i,j,k \in {1,......
NOTE ON THE DIOPHANTINE EQUATION
2007/12/13
<正> Dr.Erd(?)s conjectured that the Diophantine equation(1)x~x y~y=z~zhas no integer solution, if,x>1,y>1.z>1.In the present note,Ⅰshall prove that his conjecture is correct ouly (?)(x,y)=1 and(1)has ...