# Monthly Archives: April 2016

## Sums & Products| x+y+z=a+b+c and x*y*z=a*b*c

Note that 118 can be partitioned into three parts that have the same product in 4 different ways:     and It is the smallest number for which that is possible. Find the next smallest one.                                    ***************************************************** … Continue reading

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## When x ± y, x ± z, y ± z are squares

Find positive integers     so that the expressions are to made squares.   Here are some solutions:   ,      ,        ,      ,        ,     ,     ,     ,     , … Continue reading

## Pythagorean triples – Equal products of two legs and hypotenuse?

The following integers define two right triangles   ,     Can you find a pair of Pythagorean triples with equal products of two legs and hypotenuse:   Is it possible to find a pair of primitive Pythagorean … Continue reading

## Pythagorean triples – Equal products of two legs

The following integers define two right triangles   ,     Can you find a pair of Pythagorean triples with equal products of two legs:     Related blog:   Pythagorean triples – Equal products of a leg … Continue reading

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## Primitive Pythagorean triples: Pandigital Areas

Paul found all the 10-digit pandigital area PPT: 1458376920    {39760,   73359,   83441} 1476958230    {6660,   443531,   443581} 1498637250    {39699,   75500,   85301} 1547836290    {37765,   81972,   90253} 1567984320 … Continue reading

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## When a*b*x*y and (a^2 + b^2)(x^2 + y^2) are both squares

Here’s one possible solution: (15,   112,   113),   a Primitive Pythagorean triple, and (12,   35,   37),   also a Primitive Pythagorean triple. a = 15,   b = 112,      x = … Continue reading

## a^2+b^2, a^2+c^2, b^2+c^2

Here are the parametric equations: where     is a Pythagorean triple

## a^2+b^2+c^2, a^2+b^2+d^2, a^2+c^2+d^2, b^2+c^2+d^2

To find positive integers   a,   b,   c,   and   d   such that     Here’s a couple of examples if we let   a = d a = 120,    b = 28, … Continue reading