Let m,p be positive integers and p≥2,Fn is the Fibonacci number,q is a prime with type 4t+3,k is a nonnegative integer,for m=qk,the integer solutions of equation Fmn-1+Fmn+Fm+1=yp are given,and it is proved that the equation has no integer solutions for even number m.
Diophantine equationFibonacci sequencesum of powersinteger solutionconsecutive integers
万方数据
