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Little math problems September 2018
09-28-2018, 04:51 PM
Post: #19
RE: Little math problems September 2018
(09-25-2018 12:48 AM)Valentin Albillo Wrote:         3430000 ^2 + 10290000 ^2 = 117649000000000 = 49000 ^3
      3430000 ^3 + 10290000 ^3 = 1129900996000000000000 = 33614000000 ^2

This is how above solution (a, 3 a) is obtained:

3² + 1 = 10 = 2 * 5
3³ + 1 = 28 = 2² * 7

So, a may be the form 2x 5y 7z
Sum of square = 22x+1 52y+1 72z
Sum of square is cube, thus x=1, y=1, z=0 (modulus 3)

Sum of cubes = 23x+2 53y 73z+1
Sum of cubes is square, thus x=0, y=0, z=1 (modulus 2)

Minimum (x, y, z) that satisfy both => (4, 4, 3), thus a = 24 54 73 = 3430000
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RE: Little math problems September 2018 - Albert Chan - 09-28-2018 04:51 PM



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