Joseph Sinyor - Academia.edu (original) (raw)
I am a P. Eng. MBA (McGill) with a marketing/management career at Bell Canada (28 years).
My current interests are in mathematical research (number theory and combinatorics/computer science) and mathematics education, especially in the development of massive online open courseware (MOOC) and the use of mobile platforms.
Phone: 416-806-1832
Address: 50 Almond Ave
Thornhill, Ontario
L3T 1L2
Canada
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Papers by Joseph Sinyor
Hindawi Publishing Corporation
The 3x 1 problem can be viewed, starting with the binary form for any n ∈ N, as a string of "runs... more The 3x 1 problem can be viewed, starting with the binary form for any n ∈ N, as a string of "runs" of 1s and 0s, using methodology introduced by Błażewicz and Pettorossi in 1983. A simple system of two unary operators rewrites the length of each run, so that each new string represents the next odd integer on the 3x 1 path. This approach enables the conjecture to be recast as two assertions. I Every odd n ∈ N lies on a distinct 3x 1 trajectory between two Mersenne numbers 2 k − 1 or their equivalents, in the sense that every integer of the form 4m 1 with m being odd is equivalent to m because both yield the same successor. II If T r 2 k − 1 → 2 l − 1 for any r, k, l > 0, l < k; that is, the 3x 1 function expressed as a map of k's is monotonically decreasing, thereby ensuring that the function terminates for every integer.
We prove a combinatorial identity which arose from considering the relation r p (x,y,z) = (x + y ... more We prove a combinatorial identity which arose from considering the relation r p (x,y,z) = (x + y − z) p − (x p + y p − z p ) in connection with Fermat's last theorem.
Hindawi Publishing Corporation
The 3x 1 problem can be viewed, starting with the binary form for any n ∈ N, as a string of "runs... more The 3x 1 problem can be viewed, starting with the binary form for any n ∈ N, as a string of "runs" of 1s and 0s, using methodology introduced by Błażewicz and Pettorossi in 1983. A simple system of two unary operators rewrites the length of each run, so that each new string represents the next odd integer on the 3x 1 path. This approach enables the conjecture to be recast as two assertions. I Every odd n ∈ N lies on a distinct 3x 1 trajectory between two Mersenne numbers 2 k − 1 or their equivalents, in the sense that every integer of the form 4m 1 with m being odd is equivalent to m because both yield the same successor. II If T r 2 k − 1 → 2 l − 1 for any r, k, l > 0, l < k; that is, the 3x 1 function expressed as a map of k's is monotonically decreasing, thereby ensuring that the function terminates for every integer.
We prove a combinatorial identity which arose from considering the relation r p (x,y,z) = (x + y ... more We prove a combinatorial identity which arose from considering the relation r p (x,y,z) = (x + y − z) p − (x p + y p − z p ) in connection with Fermat's last theorem.