Andrzej Rotkiewicz

My fields are pseudoprime numbers, Lehmer numbers and diophantine equations. In my book Pseudoprime Numbers and Their Generalizations I gave all what was known about pseudoprimes up to 1972.

In the field of diophantine equations I use so called Ko-Terjanian-Rotkiewicz method to the equations connected with the Lehmer numbers and FLT (an application of the Jacobi symbol).

• Sur l'équation x^z-y^t=a^t, oú |x-y|=a, Ann. Polon. Math. 3 (1956), 7–8; MR 18 p. 561.
• On the numbers Φ(aⁿ±bⁿ), Proc. Amer. Math. Soc. 12 (1961), 419–421.
• Sur quelques généralisations des nombres pseudopremiers, Colloq. Math. 9 (1962), 109–113.
• On Lucas numbers with two intrinsic prime divisors, Bull. Acad. Polon. Sci. Sér. Math. Astronom. Phys. 10 (1962), 229–232.
• Sur les nombres premiers p et q tels que pq|2^pq-2, Rend. Circ. Mat. Palermo (2) 11 (1962), 280–282.
• Sur les chiffres initiaux et finals des nombres aⁿ et aⁿ±bⁿ, Rend. Circ. Mat. Palermo (2) 12 (1963), 150–154.
• Sur les nombres pseudopremiers de la forme ax+b, C. R. Acad. Sci. Paris 257 (1963), 2601–2604.
• (with A. Schinzel) Sur les nombres pseudopremiers de la forme ax²+bxy+cy², ibidem 258 (1964), 3617–3620.
• Sur les nombres pseudopremiers pentagonaux, Bull. Soc. Roy. Liège 33 (1964), 261–263.
• (with W. Sierpiński) Sur l'équation diophantienne 2^x-xy=2, Publ. Inst. Math. (Beograd) (N.S.) 4 (18) (1964), 135–137.
• Sur les polynômes en x qui pour une infinité de nombres naturels x donnent des nombres pseudopremiers, Atti Acad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 36 (1964), 136–140.
• Sur les nombres naturels n et k tels que les nombres n et nk sont à la fois pseudopremiers, ibidem 36 (1964), 816–818.
• Sur les formules donnant des nombres pseudopremiers, Colloq. Math. 12 (1964), 69–72.
• Sur les progressions arithmétiques et géométriques formées de trois nombres pseudopremiers distincts, Acta Arith. 10 (1964), 325–328.
• Sur les nombres de Mersenne dépourvus de diviseurs carrés et sur les nombres naturels n, tels que n²|2ⁿ-2, Mat. Vesnik 2 (17) (1965), 78–80.
• Les intervalles contenants les nombres pseudopremiers, Rend. Circ. Mat. Palermo (2) 14 (1965), 278–280.
• On the prime factors of the number 2^p-1-1, Glasgow Math. J. 9 (1968), 82–86.
• (with H. Halberstam) A gap theorem for pseudoprimes in arithmetic progression, Acta Arith. 13 (1967/68), 395–404.
• Un problème sur les nombres pseudopremiers, Nederl. Akad. Wetensch. Proc. Ser. A = Indag. Math. 34 (1972), 86–91.
• Pseudoprime numbers and their generalizations, Student Association of the Faculty of Sciences, University of Novi Sad, Novi Sad 1972, pp. i+169.
• On some problems of W. Sierpiński, Acta Arith. 21 (1972), 251–259.
• On the number of pseudoprimes ≤x, Univ. Beograd, Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 381–409 (1972), 43–45.
• On the pseudoprimes with respect to the Lucas sequences, Bull. Acad. Polon. Sci. Sér. Math. Astronom. Phys. 21 (1973), 793–797.
• The solution of W. Sierpiński's problem, Rend. Circ. Mat. Palermo (2) 28 (1979), 62–64.
• (with A. I. van der Poorten) On strong pseudoprimes in arithmetic progressions, J. Austral. Math. Soc. Ser. A 29 (1980), 316–321.
• Arithmetical progression formed from three different Euler pseudoprimes for the odd base a, Rend. Circ. Mat. Palermo (2) 29 (1980), 420–426.
• On the equation x^p+y^p=z², Bull. Acad. Polon. Sci. Ser. Math. 30 (1982), 211–214.
• On Euler Lehmer pseudoprimes and strong Lehmer pseudoprimes with parameters L,Q in arithmetic progression, Math. Comp. 39 (1982), 239–247.
• Applications of Jacobi's symbol to Lehmer's numbers, Acta Arith. 42 (1983), 163–187.
• On the congruence 2^n-2≡1 (mod n), Math. Comp. 43 (1984), 271–272.
• Problems on Fibonacci numbers and their generalizations, Applications of Fibonacci Numbers, Edited by A. N. Philippou, B. E. Bergum and A. F. Horadam, D. Reidel Publ. Comp. 1986, 241–255.
• (with A. Schinzel) On the diophantine equation x^p+y^2p=z², Colloq. Math. 53 (1986), 146–153.
• Note on the diophantine equation 1+x+x²+...+xⁿ=y^m, Elem. Math. 42 (1987), 76.
• (with W. Złotkowski) On the Diophantine equation 1 + p^α₁ + p^α₂ + ... + p^α_k = y²; in: Number Theory, vol. 11 (Budapest, 1987), North-Holland, Colloq. Math. Soc. János Bolyai, 51 (1990), 917–937.
• On strong Lehmer pseudoprimes in the case of negative discriminant in arithmetic progressions, Acta Arith. 68 (1994), 145–151.
• Arithmetical progressions formed by k different pseudoprimes, Rend. Circ. Mat. Palermo (2) 43 (1994), 391–402.
• On Lucas pseudoprimes of the form ax²+bxy+cy², Applications of Fibonacci Numbers, Volume 6, Edited by G. E. Bergum, A. N. Philippou and A. F. Horadam, Kluwer Academic Publishers, Dordrecht, 1996, 409–421.
• On the theorem of Wójcik, Glasgow Math. J. 38 (1996), 157–162.
• There are infinitely many arithmetical progressions formed by three different Fibonacci pseudoprimes, Applications of Fibonacci Numbers, Volume 7, Edited by G. E. Bergum, A. N. Philippou and A. F. Horadam, Kluwer Academic Publishers, Dordrecht, 1998, 327–332.
• Arithmetical progression formed by Lucas pseudoprimes, Number Theory, Diophantine, Computational and Algebraic Aspects, Editors: Kálmán Győry, Attila Pethő and Vera T. Sós, Walter de Gruyter, Berlin, New York 1998, 465–472.
• Periodic sequences of pseudoprimes connected with Carmichael numbers and the least period of the function l^C_x, Acta Arith. 91 (1999), 75–83.
• (with A. Schinzel) Lucas pseudoprimes with a prescribed value of the Jacobi symbol, Bull. Polish Acad. Sci. Math. 48 (2000), 77–80.