Any number of times?

Number Theory Level 1

The single digit positive integer X X satisfies this peculiar property:

If X X is multiplied by itself any number of times, then the last digit of this resultant number is still X X .

Which of the following can be possible value of X X ?

9 7 6 8

Pi Han Goh by Pi Han Goh , 30, Malaysia

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2 solutions

Toshit Jain
Mar 1, 2017

The numbers with cyclicity 1 are the possible values of X. Among the given options , only 6 has cyclicity 1 . Therefore , 6 can be the possible value of X.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Rafi Pepe
Feb 28, 2017

We try to multiply all number with itself and then we know that the one of those choices which satisfy the property is 6

1 Helpful 0 Interesting 0 Brilliant 0 Confused

No, you have not shown that 6 is the answer.

How do you know that there isn't a positive integer n n such that the last digit of 6 n 6^n is not 6?

Pi Han Goh - 4 years, 3 months ago

Your problem is not logical at all, must rethink their.

Ali Altameme - 4 years, 3 months ago

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