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. , revised by Heath-Brown , D. R. ( Oxford , 1986 ). [5] Viola , C. 1973 On the diophantine equation and Acta Arith
References [1] Cao , Z. F. 1990 On the Diophantine equation Chinese Science Bulletin 35
Abstract
For the number of integer solutions of the title equation, withW≤;x (x a large parameter), an asymptotics of the form Ax log x + Bx + O(x 1/2 (log x)3 (loglog x)2) is established. This is achieved in a general setting which furnishes applications to some other natural arithmetic functions.
purely exponential Diophantine equation (1.1) A x + B y = C z , x , y , z ∈ ℕ for some triples ( A,B,C ) with A + B = C 2 (see [ 1,3,4,6,7,9–13 ]). See also the survey paper [ 8 ], for more details about the equation (1.1) . For example
Abstract
Let a and b given unequal positive integers; it is desired to determine the positive integer solutions n and x of the equation of the title. Some special cases have recently been considered, and here some general results and conjectures are presented.
