# Monthly Archives: September 2016

## Pythagorean triangles diff. between sides,perim,diam. of inscribed circles are squares,diff. between Areas a cube

Find two Pythagorean triangles     and     such that are all squares And, the difference of areas a cube   represent the respective perimeters   the respective diameters of inscribed circles     Unfortunately, Paul’s solution … Continue reading

Posted in Number Puzzles | Tagged | 5 Comments

## Pythagorean triangle-perimeter a square and diameter of the inscribed circle a cube

Find a Pythagorean triangle with perimeter     a square and diameter of the inscribed circle a cube Let the sides be ,     ,     Then     the diameter     is to be a cube,   … Continue reading

## 2 Pythagorean triangles – sum/difference of perimeters,difference of areas are squares

Find two Pythagorean triangles the sum or difference of whose perimeters is a square, the difference of areas a square                                     … Continue reading

Posted in Number Puzzles | Tagged | 1 Comment

## Pythagorean triangles – each side is a sum of two squares

Find Pythagorean triangles each of whose sides is a sum of two squares. For example,

Posted in Number Puzzles | | 1 Comment

## (A_1)^n + (A_2)^n +…+ (A_5)^n = (B_1)^n +…+ (B_5)^n, n = 1,3,5,7

where

## 2 Pythagorean triangles (a,b,c),(d,e,f); a-b=e-f and b-c=d-e

Find two Pythagorean triangles   (a, b, c)   and   (d, e, f)   for which a – b = e – f,   and b – c = d – e           … Continue reading

## Pythagorean triangle (a, b, c): {a^2 – a, b^2 – b, c^2 – c} to be made squares

Find a Pythagorean triangle     such that the square of any side exceeds that side by a square                                       … Continue reading

## Pythagorean triangle-perimeter + square of any side is a square

Find a Pythagorean triangle the sum whose perimeter and square of any side is a square     Let the sides be   ,   where   Then are made squares where    ,    ,    , … Continue reading

Posted in Number Puzzles | Tagged | 2 Comments

## Pythagorean triangles {a^2 + b^2 ± a*b/2, a^2 + b^2 ± a*b} to be made squares

Solve (1) (2)   where     are the two odd legs in a Pythagorean triangle.                                             … Continue reading