Find x 2

Find x, y, and z such that x³+y³+z³=k for each k from 1 to 100. Write down the number of solutions.

Final Answer:

n = 35

Step-by-step explanation:

k_{1} = 3; x_{1} = 1; y_{1} = 1; z_{1} = 1 k_{2} = 10; x_{2} = 1; y_{2} = 1; z_{2} = 2 k_{3} = 10; x_{3} = 1; y_{3} = 2; z_{3} = 1 k_{4} = 10; x_{4} = 2; y_{4} = 1; z_{4} = 1 k_{5} = 17; x_{5} = 1; y_{5} = 2; z_{5} = 2 k_{6} = 17; x_{6} = 2; y_{6} = 1; z_{6} = 2 k_{7} = 17; x_{7} = 2; y_{7} = 2; z_{7} = 1 k_{8} = 24; x_{8} = 2; y_{8} = 2; z_{8} = 2 k_{9} = 29; x_{9} = 1; y_{9} = 1; z_{9} = 3 k_{10} = 29; x_{10} = 1; y_{10} = 3; z_{10} = 1 k_{11} = 29; x_{11} = 3; y_{11} = 1; z_{11} = 1 k_{12} = 36; x_{12} = 1; y_{12} = 2; z_{12} = 3 k_{13} = 36; x_{13} = 1; y_{13} = 3; z_{13} = 2 k_{14} = 36; x_{14} = 2; y_{14} = 1; z_{14} = 3 k_{15} = 36; x_{15} = 2; y_{15} = 3; z_{15} = 1 k_{16} = 36; x_{16} = 3; y_{16} = 1; z_{16} = 2 k_{17} = 36; x_{17} = 3; y_{17} = 2; z_{17} = 1 k_{18} = 43; x_{18} = 2; y_{18} = 2; z_{18} = 3 k_{19} = 43; x_{19} = 2; y_{19} = 3; z_{19} = 2 k_{20} = 43; x_{20} = 3; y_{20} = 2; z_{20} = 2 k_{21} = 55; x_{21} = 1; y_{21} = 3; z_{21} = 3 k_{22} = 55; x_{22} = 3; y_{22} = 1; z_{22} = 3 k_{23} = 55; x_{23} = 3; y_{23} = 3; z_{23} = 1 k_{24} = 62; x_{24} = 2; y_{24} = 3; z_{24} = 3 k_{25} = 62; x_{25} = 3; y_{25} = 2; z_{25} = 3 k_{26} = 62; x_{26} = 3; y_{26} = 3; z_{26} = 2 k_{27} = 66; x_{27} = 1; y_{27} = 1; z_{27} = 4 k_{28} = 66; x_{28} = 1; y_{28} = 4; z_{28} = 1 k_{29} = 66; x_{29} = 4; y_{29} = 1; z_{29} = 1 k_{30} = 73; x_{30} = 1; y_{30} = 2; z_{30} = 4 k_{31} = 73; x_{31} = 1; y_{31} = 4; z_{31} = 2 k_{32} = 73; x_{32} = 2; y_{32} = 1; z_{32} = 4 k_{33} = 73; x_{33} = 2; y_{33} = 4; z_{33} = 1 k_{34} = 73; x_{34} = 4; y_{34} = 1; z_{34} = 2 k_{35} = 73; x_{35} = 4; y_{35} = 2; z_{35} = 1 n = 35

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Showing 1 comment:

Math student

integers x, y such that
(2022, 365) = 2033x + 365y

3 years ago Like

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Find x 2

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