Question

If 17^2020 is divided by 18, then what i
remainder?
(a) 1
(b) 2
(c) 16
(d) 17​

Answer 1

Step-by-step explanation:

north of the equator is called the tropic of cancer

Answer 2

Answer:

1

Step-by-step explanation:

17^2020 = (18 - 1)^2020

There will be (2020 + 1) = 2021 terms in the expansion of {(18 - 1)^2020}. Generalized expression of the (r + 1)th term = [(2020Cr) * {18^(2020 - r)} * {(-1)^r}].

Therefore, all but one term in this expansion have 18 as their factor, hence these are completely divisible by 18.

The only term which does not have 18 as its factor happens to be that term where the exponent of 18 is zero, that is, when r = 2020, that is, the (2020 + 1)th term = 2021th term.

Now, the 2021th term = (2020C2020) * (18^0) * {(-1)^2020} = (1 * 1 * 1) = 1.

Therefore, remainder of (17^2020) divided by 18 shall be 1.