... square of any one of them added to the next following gives a square. Let the first be x, the second 2x + i, and the third 2(2*+ i)+ i or 4*rt- 3, so that two conditions are satisfied. Diophantine Analysis - Page 110by Robert Daniel Carmichael - 1915 - 118 pagesFull view - About this book
| Alexander Ingram, James Trotter (arithmetician.) - History - 1844
...which the sum is ^. 2. To find three square numbers in arithmetical progression. Ans. 1, 25, and 493. **To find three numbers such, that the square of any one of them** added to the other shall be a square. Ans. Any three fractions of which the sum is j. 4. To find two... | |
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...square. (Diophantus; Hart, 1876.) 5. Show how to find three numbers such that the product of any two **of them plus or minus the sum of the three is a square. (Diophantus.)** 6. Show how to find four numbers such that the product of each two of them increased by unity shall... | |
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...gives (4* + 3)= + x = square = (4* — 4)*, say. Therefore x = -^, and the numbers are ^, 2? ^. 33. **To find three numbers such that the square of any one of them** minus the next following gives a square. Assume x+ \, 2x+ i, 4* + i for the numbers, so that two conditions... | |
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