Question

When 25^25 is divided by 26, then what is the remainder ?

Answer 1

25(25)=(26−1)(25)25(25)=(26−1)(25)

Now use binomial expansion and expand.

We get,

25C0∗(26)25−......−(25C25)∗(1)(25)25C0∗(26)25−......−(25C25)∗(1)(25)

Now notice that all the terms have ateast one 26 except the last one. So, remainder is -1%25 which is 24.

:)

Answer 2

Remainder will be 25 only

25^25 ÷ 26 = (-1)^25 ÷ 26 = -1/26 = 26 -1 =25

using the concept of Negative Remainder