Mathematics – General Mathematics
Scientific paper
2009-08-26
Mathematics
General Mathematics
16 pages, no figures
Scientific paper
In 1998, in the winter issue of the journal Mathematics and Computer education (see [1]), Monte Zerger posed the following problem. He had noticed the Pythagorean triple (216,630,666);(216)^2+(630)^2=(666)^2. Note that 216=6^3 and 666 is the hypotenuse length. The question was then, whether there existed a digit d and a positive integer k(other than the above); such that d^k is the leglength of a Pythagorean triangle whose hypotenuse length has exactly k digits, each being equal to d. In 1999, F.Luca and P.Bruckman, answered the above question in the negative. In 2001, K.Zelator(see [2]), took this question further and showed that no Pythagorean triangle exists such that one leg has length d^k, while the other leglegth has exactly k digits in its decimal expansion, with each digit bein equal to d. In this work, we explore the above phenomenon from the point of view of number bases other than 10. We prove five Theorems. As an example, in Theorem 1, we prove that there exists no Pythagorean triangle with one of its leglengths being d^k, while the other leglength having exactly k digits in its base 4 expansion; and with digit being equal to d.
Muzaffar Habib
Zelator Konstantine
No associations
LandOfFree
Pythagorean Triangles with Repeated Digits-Repeated Bases does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Pythagorean Triangles with Repeated Digits-Repeated Bases, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Pythagorean Triangles with Repeated Digits-Repeated Bases will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-625563