Jebreel-concatenation On Pythagorean Triplets

Concatenation on SmarandachePythagorean Triplets By: Muneer Jebreel Karama SS-Math-Hebron Field Education Officer Jerusalem/Israel .box 19149 [email protected] Abstract The aim of this paper is to introduce new concepts of Concatenation on Smarandache- Pythagorean Triplets and Concatenation

on Smarandache Arithmetic Progressions and report some conjectures. Key words Concatenation on Smarandache- Pythagorean Triplets,

Concatenation on Smarandache Arithmetic Progressions. Given a familiar primitive Pythagorean triplet (3, 4, and 5), i.e. 32 + 42 =52 then, the following sequences of concatenating triplets were formulated, and called Smarandache-Pythagorean Triplets:

1) 2)

(33,44,55),(333,444,555),(3333,4444,5555), … (303,404,505),(3003,4004,5005),(30003,40004,50005),…

3)

(3030, 4040, 5050), (300300, 400400, 500500),…

4)

(33303, 44404, 55505), (333303, 444404, 555505),…

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Conjectures i) ii) iii)

There are infinitely many Smarandache-Pythagorean Triplets The reverse Smarandache-Pythagorean Triplets are Smarandache-Pythagorean Triplets. There is no Smarandache-Pythagorean Triplets primitive.

Concatenation on Smarandache Arithmetic Progressions among

Squares Given a familiar Arithmetic Progressions (A.P) among squares [1], is (1, 5, 7) i.e. 12 - 52 = 52 - 72 then, the following sequences of concatenating A.P were formulated and called Concatenation on Smarandache Arithmetic Progressions: (11, 55, 77), (111,555,777), (1111, 5555, 7777),… 2) (101,505,707),(1001,5005,7007),(10001,50005,70007),… 3) (1010, 5050, 7070), (100100, 500500, 700700),… Conjectures 1)

There are infinitely many Concatenation on Smarandache Arithmetic Progressions. II. The reverse Concatenation on Smarandache Arithmetic Progressions are Concatenation on Smarandache Arithmetic Progressions. III. There is no Concatenation on Smarandache Arithmetic Progressions consist of prime numbers. References I.

[1] K. R. Levingston, Chains of Arithmetical Progressions among squares, Journal of Recreational Mathematics 30(1999/2000), pp.52-55. [2] http://www.gallup.unm.edu/~smarandache

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