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A positive-definite ternary quadratic form does not represent all positive integers, Integers 17 (2017), #A41. (with Greg Doyle) |
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Some arithmetic convolution identities, Ramanujan Journal 43 (2017), 197-213. |
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Bounds for the representations of integers by positive quadratic forms, Mathematics Magazine 89(2) (2016), 122-131. |
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A "four integers" theorem and a "five integers" theorem, American Mathematical Monthly 122(6) (2015), 528-536. |
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Historical remark on Ramanujan's tau function, American Mathematical Monthly 122(1) (2015), 30-35. |
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Historical remark on a theorem of Zhang and Yue, Journal of Number Theory 147 (2015), 691-693. |
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The parents of Jacobi's four squares theorem are unique, American Mathematical Monthly 120(4) (2013), 329-345. |
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Arithmetic progressions and binary quadratic forms, American Mathematical Monthly 115 (2008), 252-254. (with A. Alaca and S. Alaca) |
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Berndt's curious formula, International Journal of Number Theory 4 (2008), 677-689.(with A. Alaca and S. Alaca) |
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On the representations of a positive integer by the forms x2+y2+z2+2t2 and x2+2y2+2z2+2t2, International Journal of Modern Mathematics 3 (2008), 225-230. |
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Nonexistence of a composition law, Math Mag. 80 (2007), 142-144. (with S. Alaca) |
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An arithmetic formula of Liouville, J. Théor. Nombres Bordeaux 18 (2006), 223-239. (with E. McAfee) |
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An arithmetic formula of Liouville type and an extension of an identity of Ramanujan, JP J. Algebra Number Theory Appl. 6 (2006), 33-56. (with E. McAfee) |
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Sums of six squares, Far East J. Math. Sci. 16 (2005), 17-41. (with E. McAfee) |
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Sums of sixteen and twenty-four triangular numbers, Rocky Mountain J. Math. 35 (2005), 857-868. (with J. G. Huard) |
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Infinitely many insolvable Diophantine equations, Amer. Math. Monthly 111 (2004), 909-913. (with N. Kimura) |
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n=&Delta + &Delta + 2(&Delta + &Delta), Far East J. Math. Sci. 11 (2003), 233-240. |
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Sums of twelve squares, Acta Arith. 109 (2003), 195-204. (with J. G. Huard). |
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Elementary evaluation of certain convolution sums involving divisor functions, Number Theory for the Millennium II, edited by M. A. Bennett, B. C. Berndt, N. Boston, H. G. Diamond, A. J. Hildebrand, and W. Philipp, A. K. Peters, Natick, Massachusetts, 2002, pp. 229-274. (with J. G. Huard, Z. M. Ou, and B. K. Spearman) |
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Sums of sixteen squares, Far East J. Math. Sci. 7 (2002), 147-164. (with J. G. Huard) |
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On the relative sizes of A and B in p=A²+B², where p is a prime=1(mod 4), Far East J. Math. Sci. 3 (2001), 129-132. |
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An arithmetic proof of Jacobi's eight squares theorem, Far East J. Math. Sci. 3 (2001), 1001-1005. |
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The simplest arithmetic proof of Jacobi's four squares theorem, Far East J. Math. Sci. 2 (2000), 433-439. (with B. K. Spearman) |
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On a formula of Howard, Bull. Hong Kong Math. Soc. 2 (1999), 325-340. (with B. K. Spearman) |
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Pascal's triangle (mod 8), European J. Combin. 19 (1998), 45-62. (with J. G. Huard and B. K. Spearman) |
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On Pascal's triangle modulo p2, Colloq. Math. 74 (1997), 157-165. (with J. G. Huard and B. K. Spearman) |
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Pascal's triangle (mod 9), Acta Arith. 78 (1997), 331-349. (with J. G. Huard and B. K. Spearman) |
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An arithmetic approach to the Davenport-Hasse relation over GF(p), Rocky Mountain J. Math. 25 (1995), 1341-1350. (with J. G. Huard and B. K. Spearman) |
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An elementary remark on the distribution of integers representable by a positive-definite integral binary quadratic form, Arch. Math. (Basel) 62 (1994), 38-42. (with P. Kaplan) |
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Comparison of the lengths of the continued fractions of √D and ½(1 + √D), Proc. Amer. Math. Soc. 120 (1994), 995-1002. (with N. Buck) |
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Evaluation of two trigonometric sums, Mathematica Slovaca 44 (1994), 575-583. (with Zhang Nan-Yue) |
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On the size of a solution of Legendre's equation, Utilitas Math. 34 (1988), 65-72. |
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On the solvability of the diophantine equation dV2 - 2eVW - dW2 = 1, Pacific J. Math. 124 (1986), 145-158. (with K. Hardy) |
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Pell's equations x² - my² = -1, -4 and continued fractions, J. Number Theory 23 (1986), 169-182. (with P. Kaplan) |
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On Legendre's equation ax² + by² + cz² = 0, J. Number Theory 16 (1983), 100-105. (with R. H. Hudson) |
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A divisibility property of binomial coefficients viewed as an elementary sieve, Internat. J. Math. Math. Sci. 4 (1981), 731-743. (with R. H. Hudson) |
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On the least quadratic non-residue of a prime p ≡ 3 (mod 4), J. Reine Angew. Math. 318 (1980), 106-109. (with R. H. Hudson) |
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The quadratic character of 2 mod p, Math. Mag. 49 (1976). 89-90. |
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Elementary treatment of a quadratic partition of primes p ≡ 1 (mod 7), Illinois J. Math. 18 (1974), 608-621. |
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Forms representable by integral binary quadratic forms, Acta Arith. 26 (1974), 1-9. (with P. A. Leonard) |
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On certain sums of fractional parts, Arch. Math. (Basel) 25 (1974), 41-44. (with J. M. Gandhi) |
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Another proof of a theorem of Niven, Math. Mag. 46 (1973), 39. |
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Representation of a binary quadratic form as a sum of two squares, Proc. Amer. Math. Soc. 32 (1972), 368-370. |
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Forms representable by an integral positive-definite binary quadratic form, Math. Scand. 29 (1971), 73-86. |
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Note on a theorem of Pall, Proc. Amer. Math. Soc. 28 (1971), 315-316. |
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Finite transformation formulae involving the Legendre symbol, Pacific J. Math. 34 (1970), 559-568. |
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On a result of Libri and Lebesgue, Amer. Math. Monthly 77 (1970), 610-613. |
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Quadratic polynomials with the same residues, Amer. Math. Monthly 75 (1968), 969-973. |
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A sum of fractional parts, Amer. Math. Monthly 74 (1967), 978-980. |
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An elementary number-theoretic formula, Math. Student 35 (1967), 47-50. |
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On the residues of a cubic polynomial (mod p), Canad. Math. Bull. 10 (1967), 29-38. (with K. McCann) |
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On the least non-residue of a quartic polynomial, Proc. Cambridge Philos. Soc. 62 (1966), 429-431. |
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A sum of fractional parts. II., J. Natur. Sci. and Math. 6 (1966), 209-216. |
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On the number of solutions of a congruence, Amer. Math. Monthly 73 (1966), 44-49. |
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On Norrie's identity, Math. Mag. 37 (1964), 322. |
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A note on the quadratic form ax2 + 2bxy + cy2, Math. Gaz. 48 (1964), 290-291. |
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On the factorization of the first four composite Mersenne numbers, Math. Gaz. 48 (1964), 213. |
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On the divisibility of F6 by 274, 177, Math. Gaz. 46 (1962), 315-316. |