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 A^2 = B^3 + C^3
 Set {4,b,c,d,e} such that the product of any two of them increased by 1 is a square
 smallest integer whose first n multiples all contain a 3
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 Set {2,b,c,d,e} such that the product of any two of them increased by 1 is a square
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Monthly Archives: July 2016
To make {(xy),(yz),(xz),(x+yz), (x+zy), (y+zx)}
Find three positive integers such that , , , , , are all squares … Continue reading
To make {(a+bc), (a+cb), (b+ca)} all squares, (a,b,c) in AP
Find three numbers in arithmetic progression such that (1) (2) (3) , , where the common difference is (1) ……….. (2) ……….. (3) … Continue reading
To make {(x+y+z+u),(x+y+zu),(x+yz+u),(xy+z+u),(x+y+z+u)} squares
Find four positive integers such that Hence, … Continue reading
To make {(x±y), (y±z), (z±x)} all squares
Find three positive integers such that are all squares. Here are some solutions: (A, B, C) = (2399057, 2288168, 1873432) (A, B, C) = (4387539232, 3762939168, 2433899232) (A, B, C) = (1189604889857, 680815132832, 418662940768) (A, … Continue reading
Cube expressible as a sum of consecutive cubes in two distinct ways
The sum of consecutive cubes beginning with is : The cube is expressible as a sum of consecutive cubes in two distinct ways: Can you find another example? … Continue reading
Sets of 24 consecutive squares whose sum is a square
Sets of 24 consecutive squares beginning with whose sum is a square, meaning There are six infinite families of solutions whose smallest members are : …………………………………………………….. …………………………………………………….. …………………………………………………….. …………………………………………………….. …………………………………………………….. …………………………………………………….. …………………………………………………….. …………………………………………………….. …………………………………………………….. … Continue reading
To make {(BA),(CA),(CB),(DA),(DB),(DC)} squares
To find four positive integers such that , , , , , are all squares. Here are 4 sets of solutions: Can you find other types … Continue reading
When (X,Y,Z) in geometrical progression {(XY), (XZ), (YZ)} squares
To find three rational numbers in geometrical progression, the difference of any two of which is a square number. Here’s one possible solution: The integers, form a Pythagorean triple. and the following integers, are in … Continue reading
To make {3(4m^4 – n^4), 8(9m^4 – n^4), 15(16m^4 – n^4), 24(25m^4 – n^4)} squares
To make each of the following expression squares: and are positive integers with … Continue reading
To make {(C^2 – A^2), (C^2 – B^2), (B^2 – A^2)} squares
Find positive integers such that , , , , , , are all squares. Here are some solutions: #1 : (A, B, C) = (88642, … Continue reading