Math Is Fun Forum

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,171

Fermat, computers, and a smart boy

A computer scientist claims that he proved somehow that the Fermat theorem is correct for the following 3 numbers:

x=2233445566,
y=7788990011,
z=9988776655

He announces these 3 numbers and calls for a press conference where he is going to present the value of N (to show that

x^N + y^N = z^N

and that the guy from Princeton was wrong). As the press conference starts, a 10-years old boy raises his hand and says that the respectable scientist has made a mistake and the Fermat theorem cannot hold for those 3 numbers. The scientist checks his computer calculations and finds a bug.

How did the boy figure out that the scientist was wrong?

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Fermat, computers, and a smart boy

johnathon2

Real Member

Registered: 2007-09-28

Posts: 15

Re: Fermat, computers, and a smart boy

you need to help me with my pre algebra

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great things come from great minds

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Fermat, computers, and a smart boy

well put it this way:

what is 6*6? 36

if you then look at the process of long multiplication, the last digit of any two numbers multiplied, is given by the multiplication of the 2 last digits of the numbers, because when you move onto the next digits, you move from the end: for example:

125*107 = 2125, 5*7 = 35, the 5's are the same, and that goes for any set of numbers, you can see it quite easily (just showing for integers here although it goes for non-integers too) if you look at 2 digit numbers, 'ab' and 'cd' you have the numbers 10a+b and 10c+d, which multiplied together give 100ac + 10ad + 10bc + bd, any other digits multiplied together has some power of 10 before it meaning it can't effect the last digit, which is only governed by b×d.

so showing base case of 6*6, you can then follow the above reason to say any number ending in 6 will always have last digit six at any natural power. same goes for numbers ending in 1.

atleast thats how i see it

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The Beginning Of All Things To End.
The End Of All Things To Come.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,171

Re: Fermat, computers, and a smart boy

Very Well done, Jane Fairfax and luca-deltodesco!!!

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.