The Mathematic Mistake

Sep 21, 2013

RAY: Here it is. Everyone, almost everyone remembers from his or her days in school the Pythagorean Theorem.

TOM: Yes.

RAY: A squared, plus B squared, equals C squared. And there are numbers like three, four and five; five, 12, 13 which satisfy that little equation. And many hundreds of years ago a French mathematician by the name of Fermat said, this only works for squares. He said, if you take A, B, and C, integers A, B, and C…

TOM: Yes.

RAY: And there are some A squared plus B squared that will equal C squared, and we believe that. We know we have verification of it. We got real numbers that work.

TOM: Right.

RAY: He said, if it isn't squared but it's something else like cubes or to the fourth power or to the fifth power, it doesn't work. So, for example, there is no A cubed plus B cubed, which equals C cubed. There is no A to the fourth plus B to the fourth that equals C to the fourth.

As luck would have it, a young mathematician issues a statement that he has three numbers which prove Fermat's theorem is incorrect. He calls a press conference. Now, he doesn't want to divulge everything right away. He wants to dramatize, build a little bit, does he not?

TOM: Gonna give them one number.

RAY: He gives them all three numbers. He doesn't tell the power.

TOM: Ah!

RAY: He's going to give them A, B, and C. Here are the numbers, you ready?

A equals 91. B equals 56. C equals 121.

So, it just so happens that at this little impromptu press conference, there are all these science reporters from all the po-dunky little newspapers that are around this town. And one of the guys, one of the reporters has his 10-year-old kid with him, because this happens to be a holiday. He's off from school. And the kid very sheepishly stands up and raises his hand, and he said, I hate to disagree with you, sir, but you're wrong.

The question is, how did he know?


TOM: Well, you know as I was driving home last week, the answer came to me in a flash.

RAY: Are you ten?

TOM: And I'm more than ten. I'm ten to a power. I'm ten to the N. What occurred to me was C is 121 no matter what you do that. Any power is going to end in a one. And no matter what you do to the other ones, you can't make them come out to add up to one. You can't do it.

RAY: There you go. And that's exactly what the kid saw. He said 91 to the Nth power is going to end in one.

Fifty-six to the Nth power is going to end in six. Six plus one has not to equal seven.

TOM: Not one.

RAY: The one’s digit is going to be a seven. So the one's digit of the 121 to the Nth power has got to be seven and it can't be.

TOM: It can't be.

RAY: Who's our winner this week?

TOM: The winner is Mrs. Donna Marie Markey. Wow, she gave us a whole name like that. Donna Marie Markey from Albany, New York.


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