Question

Find the remainder when 443^8421 is divided by 63?

Answer 1

Answer:

43 is congruent to 10 (mod33)

43^101 is congruent to 10^101 (mod 33.

23 is congruent to -10 (mod 33

23^101 is congruent to (-10)^101=-10^101 (mod33)

So 43^101 + 23^101 is congruent to

10^101–10^101=0 (mod 33)

Answer 2

Answer:

Step-by-step explanation:

Here $443^{8421}= (441+2)^{8421}$ All terms on expansion except $2^{8421}$ will be divisible by $63$ . because 441 is completely divided by 63.

$2^{8421}= 2^{8418}.2^3= (2^6)^{1403}.2^3= (64)^{1403}.2^3= (63+1)^{1403}.2^3$

All terms on expansion except $1^{1403}.2^3$

$1^{1403}.2^3$ means $(1)(8)=8$

hence reminder is $8$.