Nov 21, 1998
RAY: Everyone, almost everyone remembers the Pythagorean Theorem. 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.
Many hundreds of years ago a French mathematician by the name of Fermat said, this only works for squares. 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. Etc.
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?
So he gives them all three numbers. But he doesn't tell the power.
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.
RAY: Yes, you are.
TOM: I'm ten to the N.
RAY: Well, yeah, almost everyone is ten to some power.
TOM: Well, what occurred to me was C is 121, and no matter what you do that any power is going to end in a one.
RAY: There you go.
TOM: 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.
TOM: That's going to end in a one also.
RAY: 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.