find the remainder.

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Joined: Aug 4, 2011

by hemangsarkar, Sep 10, 2012, 5:37 PM

Q) the number $\frac{5^k + 3}{4}$ on division by $10$ , may leave the remainder -
$k$ is a natural number.

a) $2$

b) $6$

c) $7$

d) $8$

my solution :

we just have to plug in values of $k$ .

put $k = 1,2,3,4,5$ .

you will notice that it is $2,7 (\mod 10)$

whenever $k$ is even the remainder is $7$ , whenever it is odd the remainder is $2$ .

alternate method