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#1 2015-01-31 23:49:27

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
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Last two digits

What are the last two digits of 33^28?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
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#2 2015-02-01 00:37:14

Olinguito
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Registered: 2014-08-12
Posts: 649

Re: Last two digits

Direct calculation gives

[list=*]
[*]

[/*]
[/list]

[list=*]
[*]

[/*]
[/list]

Last edited by Olinguito (2015-02-01 00:43:57)


Bassaricyon neblina

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#3 2015-02-01 01:11:23

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Last two digits

The whole problem can be simplified down to

You can finish now easily.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#4 2015-02-01 23:06:51

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
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Re: Last two digits

How do you get to that?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#5 2015-02-02 04:29:10

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Last two digits

Thanks to Newton!


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#6 2015-02-03 03:32:37

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: Last two digits

Who is Newton?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#7 2015-02-03 04:04:56

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: Last two digits

He's an element of the set P.

Also:

When

,
is divisible by 100, so its last two digits are 00. Because of that, the last two digits of
are the same as those of

Last edited by anonimnystefy (2015-02-03 04:19:22)


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
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#8 2015-02-03 12:37:12

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Last two digits

Who is Newton?

The guy who invented the method I used.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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