Why my calculator? Why?

Is the following equation true?

178 2 12 + 184 1 12 12 = 1922 \large \color{#3D99F6}\sqrt[12]{1782^{12} + 1841^{12}} = 1922

Sometimes Yes No ...................................

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2 solutions

There are various reasons why this is wrong, though the calculator shows that it is correct. I will give you a simple introduction about this problem: it is not true, because it is a violation of Fermat's Last Theorem. This is known as a "Fermat near miss."

A calculator will tell you that two sides are equal, but there are digits of the numbers that are not equal.


For the people who don't know what is the Fermat's Last Theorem, here is a simple and quick idea:

The Fermat's Last Theorem states that there is no integer that n n can hold when n > 2 n>2 in the following equation:

x n + y n = z n \large \color{#EC7300} x^n + y^n = z^n

Getting the link to the question; the question states that:

178 2 12 + 184 1 12 = 192 2 12 \large \color{#3D99F6} 1782^{12} + 1841^{12} = 1922^{12}

Therefore this can't be true becuse it is violating the Fermat's Last Theorem so the answer to this question is No \large \color{#20A900} \text {No}


You can checkout the wiki on Fermat's Last Theorem

It is very close to true since the margin of error is 4.41 x 10^-8 For all practical purposes it is true...

Vijay Simha - 3 years, 8 months ago

BTW that explanation is wrong for fermat's theorem. It is that no POSITIVE INTEGERS can hold for x^n+y^n=z^n, n>2.

Otherwise you could just set all of them to 0.

Siva Budaraju - 3 years, 8 months ago

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Isn't that what I wrote ? " there is no integer that n can hold when n > 2 in the following equation:"

Syed Hamza Khalid - 3 years, 8 months ago

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I don't know. When I read it I didn't see the n>2 but I might just have read it wrong.

If I did, sorry about that.

Siva Budaraju - 3 years, 8 months ago

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@Siva Budaraju No problem since no one is perfect :))

Syed Hamza Khalid - 3 years, 8 months ago
Chuen-Wei Chen
Oct 3, 2017

The last digit of 1782^12 must be an even number. The last digit of 1841^12 must be 1. The last digit of 1922^12 must be an even number.

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