Tag Archives: Equation

(x^2 – 1) (y^2 – 1) = (z^2 – 1)^2

     An alternate form assuming   ,   and     are positive:     or   Here are the first few solutions:                                   … Continue reading

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Equation : (x – y)^n = x*y

    Find triplets   (x, y, n)   of positive integers such that     Note that if we set Hence   and,                                 … Continue reading

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If 60^a = 3 and 60^b = 5

                                                     

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(x + y)(x + y + 1) = k*x*y

    An interesting case of when                                81,   289,   625,   1089,   …   are of the form             … Continue reading

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(1+x)(1+x^2) = y^2

    Find all integers     such that     is a perfect square. Here are the first few solutions: ,        ,     ,        ,          Any other solutions?               … Continue reading

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tan A = tan B + tan C + tan D

      Find other   4-tuples     of distinct integers between     and     that satisfy the relation   Other solutions:     How many such equations can you produce if we allow repeated angles?   … Continue reading

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a^4 + 14 a^2 b^2 + b^4 = c^4 + 14 c^2 d^2 + d^4

    Find distinct positive integers     such that   Note that implies     Using Paul’s first few solutions:                                      

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System : {6(x^2 – y^2), 10(x^2 + y^2)}

    Give integral solutions                                                  

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(A*B*C) (A^2 + B^2 + C^2) = (D*E*F) (D^2 + E^2 + F^2)

      Find six distinct positive integers such that                                        

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(ab)(a + b)(a^2 + ab + b^2) = (cd)(c + d)(c^2 + cd + d^2)

    where     are integers   Here’s one solution:       Note that                                    

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