How Do You Determine the Unit Digit of a^b?

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Discussion Overview

The discussion revolves around determining the unit digit of the expression a^b, where a and b are positive integers. Participants explore various methods and patterns related to this problem, focusing on mathematical reasoning and potential patterns in the unit digits.

Discussion Character

  • Exploratory, Mathematical reasoning

Main Points Raised

  • One participant inquires about methods to find the unit digit of a^b.
  • Another participant suggests fixing a and varying b to identify a pattern.
  • A further response proposes that patterns may emerge, referencing specific examples like 2^2 and 2^2222, indicating a connection to divisibility.
  • Another participant seeks a more rigorous approach, prompting consideration of the values of 2 raised to increasing powers.

Areas of Agreement / Disagreement

Participants are exploring the topic with some suggesting patterns, while others seek more rigorous methods. No consensus has been reached on a definitive approach.

Contextual Notes

Participants have not yet established specific assumptions or definitions regarding the unit digit or the methods to determine it. The discussion remains open to various interpretations and approaches.

PrudensOptimus
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Hi, is there any way to find Unit Digit of a expression, say

[tex]a^b[/tex]


where a, b, are positive integers?
 
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Yes.

Hint: fix a, vary b, and ignore the irrelevant details, see if you can find a clue...
 
U mean a pattern?

Like 2^2 = 4, like 2^2222 = 4? Because 2222 is divisible by 2?
 
I mean something a little more rigorous. :smile:

Consider the values of 2^1, 2^2, 2^3, ...
 

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