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In a right triangle whose legs have integral length a and b, whose hypotenuse has integral length c, if a = 3 and c = 5, then a + c = 8, a perfect cube.  Find the least value of c greater than 5 for which a and c are relatively prime odd integers whose sum is the cube of an integer.

 Dec 12, 2019
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hint:

the first few prime odd numbers are 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79.

we also know that the ratio of a to b to c is 3:4:5.

c also have to be greater than 5.

prime odd integers whose sum is a perfect cube (1,8,27,64,125,216,etc)

 Dec 12, 2019

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