Publications-- Problems and Solutions

   
   
69. (Untitled) Solution to Problem 135, European Math. Soc. Newsletter 47 (2002), 29.
68.  (Untitled) Solution to Problem 134, European Math. Soc. Newsletter 47 (2002), 29.
67. (Untitled) Solution to Problem 130, European Math. Soc. Newsletter 45 (2002), 30.
66. (Untitled) Solution to Problem 115, European Math. Soc. Newsletter 39 (2001), 20.
65. (Untitled) Solution to Problem 112, European Math. Soc. Newsletter 39 (2001), 19.
64. "A square game," Problem 10696, proposal, Amer. Math. Monthly 105 (1998), 860; 107 (2000), 184.
63. "It keeps on growing," solution to Problem B-826, Fibonacci Quarterly 36 (1998), 86.
62. "Polynomial divisibility," solution to Problem 10452, with Roger B. Eggleton (independently), Amer. Math. Monthly 104 (1997), 977.
61. "It keeps on going," solution to Problem B-809, Fibonacci Quarterly 35 (1997), 183.
60. "Mr. Feta's Lost Theorem," solution to Problem B-808,  Fibonacci Quarterly 35 (1997), 182-183.
59. "Roots of determinant," Problem 1473, proposal, Math. Mag. 68 (1995), 147; 69 (1996), 149-150.
58. "Convex lattice pentagon," Problem 1409, proposal, Math. Mag. 65 (1992), 348; 66 (1993), 340-341.
57. "Enumeration of rationals," solution to Problem 1262, Math. Mag. 61 (1988), 119.
56. "Evaluation of a lim sup," solution to Problem E2921, Amer. Math. Monthly 93 (1986), 482-483.
55. "Taylor expansion," solution to Problem 1226, Math. Mag. 59 (1986), 298-299.
54. "Decreasing function," Problem 1253, proposal, Math. Mag. 59 (1986), 297; 61 (1988), 48.
53. "Lattice point triangles," solution to Problem 1196, Math. Mag. 58 (1985), 239-240.
52. "A fixed point theorem," solution to Problem 6409, jointly with Karl Heuer, Amer. Math. Monthly 91 (1984), 316-317.
51. "Redundancy is not always better," Problem 1116, proposed jointly with Tom Stratton, Math. Mag. 54 (1981), 84; 55 (1982), 178-179.
50. "Seven is possible," solution to Problem 1110, Math. Mag. 55 (1982), 47.
49. "Sum of (-1)^[2^n x]," solution to Problem E2813, Amer. Math. Monthly 88 (1981), 212.
48. "Old year resolution," solution to Problem 1089, jointly with Karl Heuer, Math. Mag. 54 (1981), 36-37.
47. "Int and sgn," solution to Problem 1080, jointly with Karl Heuer, Math. Mag. 53 (1980), 302.
46. "2500th digit out of 35,660," solution to Problem 1075, Math. Mag. 53 (1980), 249.
45. "Smallest root of a cubic," solution to Problem 1074, Math. Mag. 53 (1980), 248.
44. "A problem with dice," solution to Problem 1071, Math. Mag. 53 (1980), 247.
43. "A simple closed curve," Problem 1006, proposal, Math. Mag. 50 (1977), 46; 51 (1978), 306.
42. "Fixed points of iterates," solution to problem 993, Math. Mag. 51 (1978), 130.
41. "An identity in a ring," solution to Problem 991, jointly with Karl Heuer, Math. Mag. 51 (1978), 129.
40. "No polynomials," solution to Problem 990, Math. Mag. 51 (1978), 128.
39. "A trace condition," Problem 951, proposal, Math. Mag. 48 (1975) 239; 49 (1976), 256.
38. "Equal sum partitions in an Abelian group," solution to Problem 6011, jointly with C. V. Heuer, Amer. Math. Monthly 83 (1976), 750.
37. "d(A) = d(B) = 0, yet d(A + B) = 1," solution to Problem E2465, Amer. Math. Monthly 82 (1975), 405.
36. "The linear dependence of certain trigonometric values," solution to Problem E2453, jointly with Karl Heuer, Amer. Math. Monthly 82 (1975), 169-170.
35. "A generalization of the Euler-Fermat theorem," solution to Problem E2430, Amer. Math. Monthly 81 (1974), 784.
34. "Unbounded continuous functions in R^n," solution to Problem 5909, Amer. Math. Monthly 81 (1974), 674-675.
33. "The associative ring R@,  Problem 5903, proposed jointly with Albert Wilansky, Amer. Math. Monthly 80 (1973), 325; 81 (1974), 528.
32. "An irrational covering of the rationals," solution to Problem 5858, Amer. Math. Monthly 80 (1973), 952-953.
31. Solution to a generalization to Problem 851, jointly with Karl Heuer, Math. Mag. 46 (1973), 237.
30. "A prime divisor," solution to Problem 851, jointly with Karl Heuer, Math. Mag. 46 (1973), 237.
29. "Rearrangement of series," Problem E2343, proposal, Amer. Math. Monthly 79 (1972), 303; 80 (1973), 317-318.
28. "Wilsonian products in a group," solution to Problem 2303, Amer. Math. Monthly 79 (1972), 664.
27. "A determinant of primitive powers," solution to Problem E2271, jointly with C. V. Heuer, Amer. Math. Monthly 78 (1971) 1142.
26. "Extending subgroups in a group," solution to Problem 5472, jointly with C. V. Heuer, Amer. Math. Monthly 78 (1971), 799-800.
25. "A dense subset of the reals," solution to Problem E2250, Amer. Math. Monthly 78 (1971), 795-796.
24 "A conditon which implies monotonicity," solution to Problem E2246, Amer. Math. Monthly 78 (1971) 676.
23. "Partitioning sets in non-parallel hyperplanes," solution to Problem 5728, jointly with C. V. Heuer, Amer. Math. Monthly 78 (1971), 414.
22. "The integral of the reciprocal of a polynomial," solution to Problem E2236, Amer. Math. Monthly 78 (1971), 408.
21. "A dense subset of the reals,"  solution to Problem E2219, Amer. Math. Monthly 78 (1971), 80-81.
20. "The arithmetic-geometric mean inequality," solution to Problem 5686, Amer. Math. Monthly 77 (1970), 782-783.
19. "Another variation of a problem of Euler," solution to Problem E2191, Amer. Math. Monthly 77 (1970), 768-769.
18. "Fixed relations in a collection of orderings," solution to Problem 5655, Amer. Math. Monthly 76 (1969), 1158.
17. "A simple inequality," solution to Problem 5630, Amer. Math. Monthly 76 (1969), 949-950.
16. "An extension of a known inequality," solution to Problem 2117, Amer. Math. Monthly 76 (1969), 829-830.
15. "Generators of the symmetric group," solution to Problem 5610, jointly with C. V. Heuer, Amer. Math. Monthly 76 (1969) 703-704.
14. "A certain sequence of composites," solution to Problem E2062, jointly with Arne Garness and C. V. Heuer, Amer. Math. Monthly 76 (1969), 199.
13. "Counting a certain class of sequences," solution to problem E2054, Amer. Math. Monthly 76 (1969), 192-193.
12. "Rings of ordered pairs," solution to Problem 5564, Amer. Math. Monthly 76 (1969) 100.
11. "An incomplete ordered field," Problem 5551, proposal, Amer. Math. Monthly 75 (1968), 84;  1126-1127.
10. "Defining properties of a group," Problem E1873, proposed jointly with D. Bruce Erickson, Amer. Math. Monthly 73 (1966), 310; 74 (1967) 866-867.
 9. "Subrings of direct sums of copies of I_k," solution to Problem 5409, Amer. Math. Monthly 74 (1967), 744.
 8. "Nonisomorphic ordered fields," solution to Problem 5400, Amer. Math. Monthly 74 (1967), 734.
 7. "Limit points of partial sums of rearranged series," Problem 5398, proposal, Amer. Math. Monthly 73 (1966)  548;  74 (1967), 605-606.
 6. "Iterates of a Hölder function transformation," Problem 5315, proposed jointly with R. G. Lee, Amer. Math. Monthly 72 (1965), 795; 73 (1966), 790-791.
 5. "The additive identity in a simple algebraic system," Problem E1656, proposed jointly with D. Bruce Erickson, Amer. Math. Monthly 71 (1964), 90; 1134.
 4. "Variations of the basis for a normed vector space," solution to Problem 5139, Amer. Math. Monthly 71 (1964), 1048-1049.
 3. "Rings with cyclic additive group," solution to Problem 5100, jointly with D. Bruce Erickson, Amer. Math. Monthly 71 (1964), 450.
 2. "Approximating tan x with a linear fraction," Problem E1608, proposed jointly with Dean Knudson, Amer. Math. Monthly  70 (1963), 669; 71 (1964), 437-438.
 1. "Probability of a polygon," solution to Problem E1480, Amer. Math. Monthly 69 (1962), 235-236.