Qs1

Number Theory Level 2

What is the last digit of 9 2014 9^{2014} ?

3 1 9 5 7

View wiki
Sabbir Ahmed Sumon by Sabbir Ahmed Sumon , 22, Bangladesh

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

9 2014 ≡ ( − 1 ) 2014 ≡ 1 ( m o d 10 ) 9^{2014}\equiv (-1)^{2014}\equiv \boxed{1}\pmod{10}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

If x n ≡ ( y ) n ≡ a ( m o d z ) x^{n}\equiv (y)^{n}\equiv a \pmod{z} ; then does it mean that the last digit of x n x^{n} is the same as ( y ) n ⟹ a (y)^{n} \implies a ???

Syed Hamza Khalid - 2 years, 9 months ago

Log in to reply

no, but for all natural numbers a, last digit of a^x and a^(4n+x) are the same. I set the solution for the people who don't know modular arithmetic but have a good observation skill.

Sabbir Ahmed Sumon - 2 years, 8 months ago

Is it a must to choose ( m o d 10 ) \pmod {10}

Syed Hamza Khalid - 2 years, 9 months ago

9^1=9,9^2=81,9^3=729,9^4=6561. Thus if the power is odd the last digit is 9 and if it is even the last digit is 1

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...