Question

What is the remainder when is divided by 10?

Answer 1

what is divided by 10??

Answer 2

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

Answer 3

so for example 138 / 10 , the remainder is 8

Answer 4

what about 4 to 31st power ?

Answer 5

you want the remainder when dividing by 10 ?

Answer 6

yes

Answer 7

\(4^{31}\)
4^1 = 4
4^2 = 16
4^3 = 64
4^4 = 256
4^5 = 1024
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.
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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.

Answer 8

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

Answer 9

for n>=1

Answer 10

@AkashdeepDeb

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

Answer 11

there could be a way to prove it using modular math

consider 4^(2k) and 4^(2k+1)