What is the units digit of 31^3 + 13^3

B

brucejin

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I can use a calculator to find out.
But is there a better way to do this kind of question?
Thanks!
 
brucejin said:
I can use a calculator to find out.
But is there a better way to do this kind of question?
Thanks!
Click to expand...
yes.

13

13[sup:34tkmo39]2[/sup:34tkmo39] = 169

13[sup:34tkmo39]3[/sup:34tkmo39] = 2197

13[sup:34tkmo39]4[/sup:34tkmo39] = 28561

13[sup:34tkmo39]5[/sup:34tkmo39] = 371293

13[sup:34tkmo39]6[/sup:34tkmo39] = 4826809

13[sup:34tkmo39]7[/sup:34tkmo39] = 62748517

see a pattern in unit digits.......
 
Or just cube the last digit of each: 1^3 = 1 ; 3^3 = 27 ; 1 + 7 = 8
 
Based on Denis' theory, the units digits of

871^n is 1

882^4 is 6

882^3 is 8

884^4 is 6

884^5 is 4

Cool!
 
D'you think it'll be as famous as Fermat's last theorem ?
 
Thanks to denis' theorem, I now can do this units digits thing on huge numbers.

units digits of 123456789123456789123456789^4 is 1 (just do 9x9x9x9)

units digits of 2^40 is 6 (2^40 = 1024^4, so just do 4x4x4x4)

The problem is that I cannot find a big computer to check the answer.

How do I know the answer is correct?
 
brucejin said:
Thanks to denis' theorem, I now can do this units digits thing on huge numbers.

How do I know the answer is correct?
Click to expand...

Perhaps you did not know - Lord Denis has completed his quota of yearly mistakes in the month of February. So these must be correct......
 
brucejin said:
123456789123456789123456789^4

2^40

The problem is that I cannot find a big computer to check the answer.

How do I know the answer is correct? We can use "big" software on a "small" computer. 8-)
Click to expand...


Maple V Release 5 reports the following.

123456789123456789123456789^4 = 232305723727482137666188006551300203692658625799727977970043302090695104949336681913044437155857798251441

2^40 = 1099511627776

 
brucejin said:
Maple V Release 5 ?? This is Computer Algebra System (CAS) software; the current version is Maple 13.

How did you get those numbers? Your use of the prounoun "those" is ambiguous. Are you trying to ask about the numbers V and 5? :?

If you're trying to ask about the values of the two powers posted in my previous response, then I already answered your question. I "got" them using software.
Click to expand...
 
Subhotosh Khan said:
Lord Denis has completed his quota of yearly mistakes in the month of February. So these must be correct......
Click to expand...

Correct; and IT was a typo :roll:
 
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