What is the remainder when is divided by 10?

Question

What is the remainder when  is divided by 10?

gorv · Answer

what is divided by 10??

perl · Answer

any number divided by 10, the remainder is the units place , or ones place digit

perl · Answer

so for example 138 / 10 , the remainder is 8

anonymous · Answer

what about 4 to 31st power ?

perl · Answer

|dw:1414243219839:dw|

perl · Answer

you want the remainder when dividing by 10 ?

anonymous · Answer

yes

akashdeepdeb · Answer

$4^{31}$
4^1 = 4
4^2 = 16
4^3 = 64
4^4 = 256
4^5 = 1024
.
.
.


All odd powers give units place => 4
All even powers give units place => 6

Hence, 31, being odd, will give remainder as 4 when divided by 10.

perl · Answer

basically theres a pattern when you take 4^n  modulo 10 , you get alternating 4,6,4,6, ...

perl · Answer

for n>=1

perl · Answer

@AkashdeepDeb

this is an inductive argument. not a 'proof' or deductive argument

perl · Answer

there could be a way to prove it using modular math

consider 4^(2k)  and  4^(2k+1)

ganeshie8 · Answer

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