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http://hdl.handle.net/2080/1845| Title: | Arithmetic progression of squares and solvability of the diophantine equation 8x4 + 1 = y2 |
| Authors: | Panda, G K |
| Keywords: | Balancing numbers Diophantine equations Recurrence relations Arithmetic progressions |
| Issue Date: | Oct-2012 |
| Citation: | International Conference in Number Theory and Applications, Mathematics, Kasetsart University, Bangkok, Thailand, October 24-26, 2012. |
| Abstract: | There is no arithmetic progression consisting of square terms and with a square common di erence. Alternatively, the diophantine equation 1 + x4 = 2y2 has no solution in positive integers. Consequently, the diophantine equation 8x4 + 1 = y2 has no positive integral solution other than x = 1; y = 3, a clear indication that no balancing number other that 1 is a perfect square. |
| Description: | Copyright belongs to proceeding publisher |
| URI: | http://hdl.handle.net/2080/1845 |
| Appears in Collections: | Conference Papers |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| full_paper.pdf | 263.45 kB | Adobe PDF | View/Open |
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