O uzastopnim palidromima

In this paper, we will try to characterize consecutive palindromes - positive integers simultaneously palindromic in multiple consecutive number bases. We search for solutions in the cases of two and three number bases and observe the fact that solutions likely do not exist in the case of four or more number bases. In practice, this requires solving systems of corresponding linear Diophantine equations. This was motivated by the question Can a positive integer be palindromic in more than three consecutive number bases?. The question does not appear to have an obvious approach and remains open. The analysis of consecutive palindromes in three number bases suggests that the answer to the question is likely negative.U ovom radu pokušatćemo karakterizirati uzastopne palindrome - brojeve koji su istovremeno palindromčni u všestruko uzastopnih brojevnih baza. Tržimo rješenja u slučajevima dvije i tri brojevne baze, te promatramo činjenicu kako rješenja vjerojatno ne postoje u slučaju četiri ili više brojevnih baza. U praksi, ovo zahtjeva rješavanje sustava odgovarajućih linearnih Diofantskih jednadžbi. Ovaj rad je motiviralo pitanje Može li broj biti palindromičan u više od tri uzastopne brojevne baze? Čini se kako pitanje nema očit pristup te ostaje otvoreno. Analiza uzastopnih palindroma u tri brojevne baze upućuje nas na to da bi odgovor na postavljeno pitanje bio negativan