engleski

On a conjecture regarding balancing with powers of Fibonacci numbers

Here, we show that (k, l, n, r) = (8, 2, 4, 3) is the only solution in positive integers of the Diophantine equation F_1^k + F_2^k + ... + F_{; ; n-1}; ; ^k = F_{; ; n+1}; ; ^k + ... + F_{; ; n+r}; ; ^k where F_m is the mth Fibonacci number.

Fibonacci numbers ; linear forms in logarithms ; LLL algorithm

nije evidentirano