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Computing Powers of Positive Integers Using the Modified Detached Coefficients Method and the Staircase Method.
A Thesis presented to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE INDUSTRIAL MATHEMATICS Institute of Distance Learning.June,2013
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| Format: | Thesis |
| Language: | English |
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2014
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| _version_ | 1867613137131274240 |
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| access_status_str | Open Access |
| author | Avoka, John |
| author_browse | Avoka, John |
| author_facet | Avoka, John |
| author_sort | Avoka, John |
| collection | Thesis |
| description | A Thesis presented to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in Partial Fulfillment of the Requirements for the
Degree of
MASTER OF SCIENCE
INDUSTRIAL MATHEMATICS
Institute of Distance Learning.June,2013 |
| format | Thesis |
| id | oai:ir.knust.edu.gh:123456789/5476 |
| institution | KNUST (Ghana) |
| language | English |
| last_indexed | 2026-06-10T12:31:21.331Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from KNUSTSpace — Kwame Nkrumah University of Science & Technology (Ghana) |
| publishDate | 2014 |
| publishDateRange | 2014 |
| publishDateSort | 2014 |
| record_format | dspace |
| source_str | KNUSTSpace — Kwame Nkrumah University of Science & Technology (Ghana) |
| spelling | oai:ir.knust.edu.gh:123456789/5476 Computing Powers of Positive Integers Using the Modified Detached Coefficients Method and the Staircase Method. Avoka, John A Thesis presented to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE INDUSTRIAL MATHEMATICS Institute of Distance Learning.June,2013 The Modified Detached Coefficients Method is used to find power numbers ,say Q = (d1d2…dm)n to any positive nth power. The power number is first converted to a multinomial, Say Q= (d1d2d3)3 Q = (d1pm-1 +d2pm-2 +dmp0)n…(1),where m is the number of digits and n is a positive power of the expansion. Then equation (1) is expanded using the multinomial expansion. The coefficients (d’s) of the p’s are extracted to become the result of the power number if and only if all the coefficients are single digits otherwise convert the coefficients which are more than 1 to p’s by replacing 10’s by p. For example, supposing 54 is a coefficient it is replaced by 5p+4,i.e. 5*10+4 =5*p+4. Where 10=p. The Staircase Method is also used to find power numbers. The procedure is the same as the Modified Detached Coefficients Method but after the expansion of the converted form of the power number. The coefficients (d’s) of the p’s are arranged in the staircase form. The result of the power number is then gotten by adding the staircase numbers arrangement column wise as done in multiplication of two numbers. Results of both methods were done manually. KNUST 2014-01-08T15:56:37Z 2023-04-20T20:00:04Z 2014-01-08T15:56:37Z 2023-04-20T20:00:04Z 2013-06-08 Thesis https://ir.knust.edu.gh/handle/123456789/5476 en application/pdf |
| spellingShingle | Avoka, John Computing Powers of Positive Integers Using the Modified Detached Coefficients Method and the Staircase Method. |
| title | Computing Powers of Positive Integers Using the Modified Detached Coefficients Method and the Staircase Method. |
| title_full | Computing Powers of Positive Integers Using the Modified Detached Coefficients Method and the Staircase Method. |
| title_fullStr | Computing Powers of Positive Integers Using the Modified Detached Coefficients Method and the Staircase Method. |
| title_full_unstemmed | Computing Powers of Positive Integers Using the Modified Detached Coefficients Method and the Staircase Method. |
| title_short | Computing Powers of Positive Integers Using the Modified Detached Coefficients Method and the Staircase Method. |
| title_sort | computing powers of positive integers using the modified detached coefficients method and the staircase method |
| url | https://ir.knust.edu.gh/handle/123456789/5476 |
| work_keys_str_mv | AT avokajohn computingpowersofpositiveintegersusingthemodifieddetachedcoefficientsmethodandthestaircasemethod |