Let M(m, n) be the integer sequence of all positive measurable amounts less than m + n that are obtainable by two unmarked jugs with capacities m and n units. We introduce the concept of dual sequences which describe the correspondence relation between M (m₁, n₁) and M (m₂, n₂), where 0 < m₁ < n₁, 0 < m₂ < n₂, m₁ + n₁ = m₂ + n₂ and gcd (m₁, n₁) = gcd (m₂, n₂) = 1. Some illustrative examples are provided. Copyright © 2018 Research India Publications.
|Title of host publication||Advanced mathematics: Theory and applications|
|Place of Publication||Delhi, India|
|Publisher||Research India Publications|
|ISBN (Print)||9789387374331, 9387374335|
|Publication status||Published - 2018|
CitationMan, Y.-K. (2018). On dual sequences of measurable amounts of the two jugs problem. In T. Kim (Ed.), Advanced mathematics: Theory and applications (Vol. II, pp. 13-22). Delhi, India: Research India Publications.
- Jug problem
- Dual sequence
- Measurable amounts
- Diophantine equation