# 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

## (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

## 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