The unit digit

Level pending

Find the unit's digit in 3 1 197 31^{197} + 2 5 303 25^{303} + 5 0 55 50^{55} - 4 6 67 46^{67}


The answer is 0.

Arpit Sah by Arpit Sah , 22, India

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

Jubayer Nirjhor
Dec 21, 2013

3 1 197 + 2 5 303 + 5 0 55 − 4 6 67 \nonumber ≡ 1 + 5 + 0 − 6 ( m o d 10 ) \nonumber = 0 \LARGE{\begin{aligned} &~ &31^{197}+25^{303}+50^{55}-46^{67} \nonumber \\ \\ &\equiv ~~~& 1 + 5 + 0 - 6 \pmod{10} \nonumber \\ \\ &= ~~~ & \fbox{0} \end{aligned}}

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Azizul Islam
Dec 24, 2013

unit's digit of 31^n, 25^n, 50^n and 46^n always be 1, 5, 0 and 6 respectively ; where n>1,

1+5+0-6=0

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...