The remainder when 7^{2022} + 3^{2022} is div | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) We need to find the remainder of $7^{2022} + 3^{2022}$ when divided by $5$.Note that $7 \equiv 2 \pmod{5}$ and $3 \equiv -2 \pmod{5}$.Thus,$7^{202

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) We need to find the remainder of $7^{2022} + 3^{2022}$ when divided by $5$.Note that $7 \equiv 2 \pmod{5}$ and $3 \equiv -2 \pmod{5}$.Thus,$7^{2022} + 3^{2022} \equiv 2^{2022} + (-2)^{2022} \pmod{5}$.Since $2022$ is an even number,$(-2)^{2022} = 2^{2022}$.So,$7^{2022} + 3^{2022} \equiv 2^{2022} + 2^{2022} = 2 	imes 2^{2022} = 2^{2023} \pmod{5}$.We know that $2^4 = 16 \equiv 1 \pmod{5}$.Therefore,$2^{2023} = 2^{4 	imes 505 + 3} = (2^4)^{505} 	imes 2^3 \equiv 1^{505} 	imes 8 \equiv 8 \pmod{5}$.Finally,$8 \equiv 3 \pmod{5}$.The remainder is $3$.

The remainder when $7^{2022} + 3^{2022}$ is divided by $5$ is:

Similar Questions

The remainder when $3^{100} \times 2^{50}$ is divided by $5$ is

The remainder obtained when the polynomial $x^{64} + x^{27} + 1$ is divided by $(x + 1)$ is

For all positive integers $k$, if the greatest divisor of $25^k+12k-1$ is $d$, then $4\sqrt{d}=$

If $P(n):$ " $2^{2n}-1$ is divisible by $k$ for all $n \in N$ " is true,then the value of $k$ is:

The remainder,when $7^{103}$ is divided by $17$ is $..........$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module