Question

whats the remainder when 25^25 is divided by 26

Answer 1

Well, you can take this approach :

2525=(26−1)252525=(26−1)25

Using Binomial Theorem[1] , you know that every term in the expansion contains powers of 26 except this one : (2525)(2525) (26)0(−1)25(26)0(−1)25

Clearly, the above term is -1 and the remainder is 25.25.Think why?

Or you can take this approach :

Footnotes

[1] Binomial theorem - Wikipedia

Answer 2

Answer:

Find the values of k for which the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k – 1, 5k)

are collinear.