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No software allowed ! (Posted on 2017-05-07) Difficulty: 3 of 5
Find positive integers a, b, and c, all different, such that
a^3 + b^3 = c^4.

Please obey the title !

No Solution Yet Submitted by Ady TZIDON    
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Solution Solution | Comment 1 of 6
Let x,y,z be any set of positive integer satisfying z=x^3+y^3.  Then c=z, a=x*z, b=y*z is an integral solution to a^3 + b^3 = c^4.

For example, 2^3+3^3=35 makes (x,y,z)=(2,3,35) Then (a,b,c)=(70,105,35) yields 70^3+105^3=35^4=1500625.

  Posted by Brian Smith on 2017-05-07 10:09:40
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