Kenneth S. answered • 03/20/17
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numbers are divisible BY other numbers, not "to" them.
Since the assertion 3n + 1 = 8k is what is being proposed, where k is some integer, we should test it to see if it's ever true. Letting n=1, we see that 3+1 = 8k has no integer solution. One counterexample is enough to discredit the proposition, so we have shown it not to be true, in general.
Kenneth S.
I think that you're right, Arturo, I just based my reaction on the title!
My Number Theory course was in 1958 at Stanford, taught by Prof. Szego, famed Hungarian math prof who was John von Neuman's tutor in Budapest when John was a very young person. Von Neuman is considered to be one of the founders of computers, a field that I entered in 1957. My number theory knowledge has now shrunk to almost nothing.
Small world!
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03/20/17
Arturo O.
Kenneth,
The little number theory I had was in the introduction to a 1 semester basic course in modern algebra in 1976, and I never dealt with it since then. We need a number theory person to tackle this problem.
I am familiar with von Neumann's work in Monte Carlo methods. I used some of his methods in my MS thesis in physics at Cal State Northridge, which involved Monte Carlo simulation of Compton gamma ray scattering and neutron scattering.
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03/21/17
Kenneth S.
Arturo, I told you it was a small world! I lived in Northridge 5 years, and taught programming languages there for a couple of years, around the time of the 1971 earthquake. My first daughter got her Psychology B.S. there, and also her Masters (her mentor was Dr. Doctor!!).
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03/21/17
Arturo O.
Kenneth,
A small world indeed. And considering that many of the math questions are from the Southern California area, we might be interacting with a few CSUN students!
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03/21/17
Arturo O.
03/20/17