Diophantine Analysis

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John Wiley & sons, Incorporated, 1915 - Diophantine analysis - 118 pages
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Page 106 - To find three squares such that the product of any two of them, added to the sum of those two, gives a square.
Page 112 - ... 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.
Page 112 - ... and c. 35. The edges of two hollow cubes differ by 10 centimeters. If a certain quantity of water is poured into the larger cube, there remain 1578 cubic centimeters of space not filled with water. If the second cube contained 142 cubic...
Page 116 - F(x) denotes an irreducible polynomial in x of degree r (r>z) with integral coefficients and c is an integer, has only a finite number of solutions in integers p and q.
Page v - They can be got from right-angled triangles2 by dividing the square of one of the sides about the right angle by the square of the other. Let the squares then be The continued product = -J^ffax...
Page 97 - ... z, which are prime each to each, then one of these integers (say z) and the sum of the other two (say x-\-y) are both divisible by q. We shall give one other theorem which may be demonstrated by elementary means; namely, the following: V. // p is an odd prime and the equation...
Page 115 - ... the product of two sums of eight squares as a sum of eight squares.