Problems need HardWork #14

Number Theory Level 2

Find the unit digit of 2^2^2^2^...... (100 times)


The answer is 6.

Dev Sharma by Dev Sharma , 20, India

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1 solution

Dev Sharma
Aug 25, 2015

The number of the form 2^(4n) has 6 as its last digit.

4 Helpful 0 Interesting 0 Brilliant 0 Confused

You need to explain why it's true for all 4n. And not based on the first few values of n.

Pi Han Goh - 5 years, 9 months ago

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2^4 = 6 mod10

(2^4)^n = 6^n mod10

2^4n = 6 mod 10

Dev Sharma - 5 years, 9 months ago

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