Question

If (2021)3762 is divided by 17, then the remainder is​

Answer 1

We have to find the remainder if $(2021)^{3762}$ is divided by 17.

solution : just write 2021 in the form of 17.

we get, 17 × 119 - 2 = 2021

we see if we divide 2021 or 17 × 119 - 2 we get, remainder -2

so if$(2021)^{3762}$ is divided by 17.

we get, $(-2)^{3762}$ as remainder.

but this is not a number less than 17.

we ''ll again divide $(-2)^{3762}$ by 17.

but here we see, 2⁴ = 6

so, $(-2)^{3762}=(-2)^{2}(-2)^{3760}=4.\{(-2)^4\}^{\frac{3760}{4}}$

= $4.(16)^{940}$

now divide $4.(16)^{940}$ by 17

we get, remainder = $4(-1)^{940}$ = 4

Therefore the remainder would be 4.