Question

Find the remainder of 51⁵¹ when divided by 25.

Answer 1

We have, 51⁵¹ = (50 + 1)⁵¹ 

Now, if we expand this expression all the terms expect the constant (last) term will contain 50.

Thus will leave no remainder upon division by 25, the last term will be (1)51 = 1

Thus, remainder is 1