Question

50^51^52 /11
a)6
b)4
c)7
d)3
ans is 6 but expln in detail

Answer 1

Answer: 6

Step-by-step explanation:

Using the Fermat's little theorem, we know that any number co-prime to 11 raised to the power of 10 gives a remainder of 1 when divided by 11, i.e.

a^10=1(mod 11), if a is co-prime to 11.

Now since 50 is co-prime to 11, the idea is to write 51^52 in the form of 10*p+q.

Now,

51^52=1(mod 10)

Since 51=1(mod 10)

Therefore 51^52 can be written as 10*p +1

And the original equation can be replaced with

50^(10*p+1).

Now 50^10=1(mod 11)

Therefore,

50^(10p+1)=50(mod 11)=6(mod 11)

Therefore,

50^51^52=6(mod 11).

So the answer is 6.