Tag Archives: Pythagorean Triples

Pythagorean triangle {a+b+c, a^2+b+c, a+(b+c)^2} are to made squares

    Find a Pythagorean triangle     such that     are all squares                                                   … Continue reading

Posted in Number Puzzles | Tagged | Leave a comment

Set of 3 Pythagorean triangles equal perimeters and area in A.P.

    Here are sets of 3 Pythagorean triangles with equal perimeters and area in arithmetic progression. Note that the perimeters are multiples of 120.      The pattern breaks in this example: The perimeter is not a multiple of … Continue reading

Posted in Number Puzzles | Tagged , | 2 Comments

Pythagorean triples – Equal products of a leg and hypotenuse

    The following integers define two right triangles   ,    .   Equal products of a leg and hypotenuse :   Here are some solutions:   (3504, 21172, 21460),    (7104, 7847, 10585) …..   (278588, 14784, 278980), … Continue reading

Posted in Number Puzzles | Tagged | Leave a comment

Pandigital Pythagorean triples

    Pythagorean triples   (546,728,910),   (534,712,890)   each involve nine distinct digits   (546,   728,   910)    =    182 × [3, 4, 5] Perimeter   =   2184 Area   =   198744   (534, … Continue reading

Posted in Number Puzzles | Tagged , | Leave a comment

Pythagorean triples of the form (x, y, y+50)

                                   

Posted in Number Puzzles | Tagged | Leave a comment

Pythagorean triples (a,b,c), (x,y,z) and (z+c)^2 – (x+a)^2 – (y+b)^2

  The integers form a Pythagorean triple So do these integers   Consider   The expression gives us The expression      is a square   Expression #2 :    Expression #3 :    Expression #4 :    Expression #5 … Continue reading

Posted in Number Puzzles | Tagged | Leave a comment

Pythagorean triples (a, b, c); where c – b = 8 (a, b, c); where c – b = 8

  The integers with   form a Pythagorean triple   that is,         Area   : Perimeter   : semiperimeter   :                    

Posted in Number Puzzles | Tagged | Leave a comment

Pythagorean triples (a, b, c=b+2)

    The integers form a Pythagorean triple   Perimeter   : where     is the n-th triangular number   Area   : we note that that is,                        … Continue reading

Posted in Number Puzzles | Tagged | Leave a comment

Pythagorean triples of the form (x^2 – 1, 2*x, x^2 + 1)

  The integers   ,    ,      form a Pythagorean triple. where     (3, 4, 5)   :   primitive ,      ,        (8, 6, 10)   =   2[4, 3, 5]   (15, 8, … Continue reading

Posted in Number Puzzles | Tagged | Leave a comment

Diophantine equation: x^2 + y^2 = z^2 + 1 (Almost Pythagorean Triples)

    A Pythagorean triple (PT) is an ordered triple   (a, b, c)   that satisfies the Pythagorean equation:     Find an ordered triple   (x, y, z)   that satisfies the Diophantine equation where   x,   … Continue reading

Posted in Number Puzzles | Tagged , | 7 Comments