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- Feb 14, 2012

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Find \(\displaystyle M\) and also the unit digit of \(\displaystyle M^{2003}\).

- Thread starter anemone
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- Thread starter
- Admin
- #1

- Feb 14, 2012

- 3,813

Find \(\displaystyle M\) and also the unit digit of \(\displaystyle M^{2003}\).

- Aug 30, 2012

- 1,162

Just a moment and I'll have it. I just have to program Excel...

Find \(\displaystyle M\) and also the unit digit of \(\displaystyle M^{2003}\).

-Dan

- Mar 31, 2013

- 1,334

We are taking square root of |x| - 2 and its –ve so it has to be zero

Find \(\displaystyle M\) and also the unit digit of \(\displaystyle M^{2003}\).

So |x| - 2 = 0 or x = 2 or – 2

x cannot be 2 as |2-x| is in denominator

so x = - 2

hence putting the value x = -2 we get M = 7

as M^4 = 1 mod 10

M^2000 = 1 mod 10 or M^2003 = M^3 mod 10 = 343 mod 10 or 3

3 is the unit digit

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- #4

- Feb 14, 2012

- 3,813

HiWe are taking square root of |x| - 2 and its –ve so it has to be zero

So |x| - 2 = 0 or x = 2 or – 2

x cannot be 2 as |2-x| is in denominator

so x = - 2

hence putting the value x = -2 we get M = 7

as M^4 = 1 mod 10

M^2000 = 1 mod 10 or M^2003 = M^3 mod 10 = 343 mod 10 or 3

3 is the unit digit

Thanks for taking the time to participate in this challenge problem and I can tell how much you enjoyed working with some of the problems that I posted here and in case if you have any interesting mathematics problems to share with us,

HiJust a moment and I'll have it. I just have to program Excel...

-Dan

Thank you for the reply and you know what, you're one of the clever \(\displaystyle \cap\) humorous member at MHB!