Problems & Puzzles:
Pythagorean triangles again -II
From the sequences
and A245648, Ivan
Ianakiev sends the following nice puzzle, originally in
Bulgarian, alike the
The problem 81
was posed by
Sierpinski over 70 years ago and no one has found another
I'd like to present a similar problem of
a) is newer and
b) has several visible solutions (see OEIS A245646, A245647,
A245648), which might (or might not) suggest they are easier
The Pythagorean triple (3,4,5) consists of the triangular
number 3, the square number 4 and the pentagonal number 5.
Other such triples are (9,12,15), (100,105,145) and
Can you find more like these four already found?
Please notice that the order of
the triangular, square and pentagonal integers may vary from triplet
On week 14-20, March 2021, contributions came from Emmanuel
Simon Cavegn wrote:
Found no more than the known solutions.
My program's search space was [first 233000 triangular numbers] x
[first 1000000 pentagonal numbers]