Tag Archives: Sums of 4-th Powers

A^4 + B^4 + C^4 = 2 × D^4

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Equation : a^4 – b^5 = c^5 – d^4

    Let     be positive integers,   with   ,   and   Prove that if   ,   then twice the sum of the 5-th powers is a sum of two squares.           … Continue reading

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a^4 + 4*b^4 = c^4 + 4*d^4

      are distinct integers,    and                                         

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A^4 + B^4 = C^4 + D^4 + E^4

        ……………………………………………………… ……………………………………………………… ………………………………………………………     Find other solutions for   A < 100718                          

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Equation: a^4 + b^4 ± k = c^2

    where   k   is a small odd integer.   k = +3   k = -7   k = +7     Find other solutions where k is a small odd integer.           … Continue reading

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Equation: a^4 + b^4 = c^2 + 1

    where   a, b, c   are integers             Paul found:                                  

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a^4 – b^4 = c^4 – d^4 = e^4 – f^4

        for example,   (1) …… ……. ……..   (2)   …..     …..     ……     (3)   …..     …..     …..     In each of the 3 pairs … Continue reading

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Part 2 – N^4 = 2(A^4) + B^4 + 2(C^4)

    Previous blog:   A^4 + B^4 + C^4 + D^4 + E^4 = N^4     for                                            … Continue reading

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A^4 + B^4 + C^4 + D^4 + E^4 = N^4

                                                                                              Paul found:    … Continue reading

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A^4 + B^4 + C^4 + D^4 = N^2

      Can you find smaller values?                                

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