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## Topic review (newest first)

bobbym
2013-06-17 02:37:43

I have been waiting. There are 3 basic ways.

1) Do some raising of a power and play spot the pattern.

2) Repeated squaring.

3) Use the binomial theorem.

1) Did not yield anything I could do. Which of 2 and 3 would you like?

Agnishom
2013-06-17 02:34:57

I can't handle either cases.

How do you do it?

[This problem is not meant for a computer]

phrontister
2013-06-17 01:14:54

Hi Agnishom,

641

bobbym
2013-06-17 01:12:11

Hi;

Agnishom
2013-06-17 00:39:41

New Problem
Compute the last 3 digits of 171^172.

phrontister
2013-06-17 00:33:31

Hi stefy,

I couldn't find any others either.

anonimnystefy
2013-06-16 22:16:14

#### bobbym wrote:

You mean of the type

3^(xxxxxx)?

Nearly. It is y^(xxxxxx). x and y are single-digit integers >0, and y may = x.

So the test is this:
For a=y^(xxxxxx) and b=y(x+x+x+x+x+x), the middle digit for Length[a]=odd (or the middle two digits for Length[a]=even) = b.

So far, after not looking any further than my example in post #14, all I've found is just that one solution.

There are no such numbers besides x=5 and y=3.

bobbym
2013-06-16 21:55:36

The last digit can be done by mods. The first digit is usually just raw computation except in specific cases. The middle digits are like the first digit.

phanthanhtom
2013-06-16 21:49:22

How did you calculate all this?

bobbym
2013-06-16 20:39:23

Hi;

Okay, let me know if you find one more.

phrontister
2013-06-16 20:22:51

No others.

It was only something completely frivolous where the numbers just happened to fall into place, but now I've set it up like this I might see if there are other solutions...if only to exercise my M.

bobbym
2013-06-16 20:06:01

How many have you looked at?

phrontister
2013-06-16 20:04:01

#### bobbym wrote:

You mean of the type

3^(xxxxxx)?

Nearly. It is y^(xxxxxx). x and y are single-digit integers >0, and y may = x.

So the test is this:
For a=y^(xxxxxx) and b=y(x+x+x+x+x+x), the middle digit for Length[a]=odd (or the middle two digits for Length[a]=even) = b.

So far, after not looking any further than my example in post #14, all I've found is just that one solution.

bobbym
2013-06-16 13:45:22

You mean of the type

3^(xxxxxx)?

phrontister
2013-06-16 13:39:58

As far as I know (after having done just one test like this), my example is unique and doesn't extend to other sums.