Monthly Archives: December 2016

Antimagic Square 4X4

    An antimagic square is an     array of integers from  1   to     such that each row, column, and main diagonal produces a different sum such that these sums form a sequence of consecutive integers. … Continue reading

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Make {x^2 + 3xy + y^2, x^2 + 5xz + z^2, y^2 + 7yz + z^2} squares

                                                                                #1                           Here are the first few solutions:                                                                                 #2                                                                                                           #3                                 the first few solutions:                                                                               #4                           … Continue reading

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Make {x^2 – 2xy + y^2, x^2 – 3xz + z^2, y^2 + 5yz + z^2} squares … Part 3

    Find three positive integers     such that     and   Here are the first few solutions     find the next few solutions                           … Continue reading

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Make {x^2 – 2xy + y^2, x^2 + 3xz + z^2, y^2 – 5yz + z^2} squares … Part 2

    Find three positive integers     such that     and   Here are the first few solutions:       Find the next few solutions.                         … Continue reading

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Make {x^2 + 2xy + y^2, x^2 + 3xz + z^2, y^2 – 5yz + z^2} squares … Part 1

    where     are positive integers.   Here are the first few solutions:     Find the next few solutions.                                     … Continue reading

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To make {x^2 + y^2 – 1, x^2 – y^2 – 1} squares

    Find two distinct positive integers     to make the two expressions squares       Here’s one family of solutions:                                                                                                                                                and another family of solutions                 … Continue reading

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Make {(x^2 + x*y + y^2), (x^2 – x*z + z^2), (y^2 + y*z + z^2)} squares … Part 5

      These are the first few solutions I found:                                                    

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Make {(a^2 + 12*b^2), (12*a^2 + b^2)} squares

      Find distinct positive integers     such that       Paul found and their multiples                                           … Continue reading

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Make {(x^2 – xy + y^2), (x^2 – xz + z^2), (y^2 – yz + z^2)} squares … Part 4

    Find distinct integers     to make the three expressions squares       (1) Pipo found:     (2)   Here’s another set of solutions                         … Continue reading

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Make {(x^2 + xy + y^2), (x^2 – xz + z^2), (y^2 – yz + z^2)} squares … Part 3

    Find distinct integers     to make the three expressions squares                                                      

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