| John Bonnycastle - Algebra - 1811 - 220 pages
...proportion. Ans. 1225, 49, and 25. 14. To find three numbers in arithmetical progression, such that **the sum of every two of them may be a square number.** Ans. 120-J, 840i,ond I560£. 15. To find three numbers, such that, if to the square of each of them... | |
| Thomas Leybourn - Mathematics - 1817
...case. vi. QUESTION 974, by Mr. James Cunliffe, Weslhoughton. To find three whole numbers such, that **the sum of every two of them may be a square number,** and also that their squares may be in arithmetical progression. Answered by Amiens. Let a* + 2a*o"... | |
| John Ryley, John Gawthorp, John Whitley - Mathematics - 1818 - 4 pages
...(143,) By Mr. JOHN BAINES, Jun. . Find three numbers in arithmetical progression such than n times **the sum of every two of them may be a square number.** Answeredby MR. E. WEBSTER, Armley Mills. Suppose x — y,x,and *+^tobe'the required numbers. t(2x+y-)xn=p''nn... | |
| James Thomson - History - 1844
...4x, and 2* + 1, as the required numbers, and he thus obtains very simply the answers here given. 9. **Required three numbers, such that the sum of all three, and the sum of every** pair of them, may be square numbers. An,. K«2—l), T,V(t,.2—i)2_|(t.2—i), and 10. Render fa:3... | |
| James Bates Thomson - Algebra - 1845 - 308 pages
...4x, and 2x+ 1, as the required numbers, and he thus obtains very simply the answers here given. 9. **Required three numbers, such that the sum of all three, and the sum of every** pair of them, may be square numbers. An*. K«2-l), TIW«2-1)2-K«2-l)> *"* i(«2 + 2). 10. Render G^... | |
| C. Gill - Diophantine analysis - 1848 - 90 pages
...and taking ¿ = 82, we have x = 6242, у =3362, z =482. PROBLEM. VII. To find four numbers, such that **the sum of every two of them may be a square number.** ¿Solution. The equations to be solved are and they give These last equations may be solved by Prob.... | |
| Industrial arts - 1851
...solutions to three Diophantine Problems, the first of which finds "three square numbers, such that **the sum of every two of them may be a square number** ;" the second determines " values for the sides of a triangle in whole numbers, such that the lengths... | |
| J.C. ROBERTSON - 1851
...solutions to three Diophantine Problems, the first of which finds "three square numbers, such that **the sum of every two of them may be a square number;"** the second determines " values for the sides of a triangle in whole numbers, such that the lengths... | |
| Sholto Percy - Industrial arts - 1851
...solutions to three Diophantine Problems, the first of which finds " three square numbers, such that **the sum of every two of them may be a square number;"** the fécond determines "values for the sides of a triangle in whole numbers, such that the lengths... | |
| Mathematics - 1893
...elsewhere has been made the subject of a dispute.] 731. (Amicus.) — Find three numbers such that **the sum of every two of them may be a square number,** and that the sum of the three squares thus found may be also a square number. 741. (JW Elliott.) —... | |
| |