Question

find the remainder when 1021^1022 is divided by 1023?​

Answer 1

Answer:

What's the remainder if 1022^1023 is divided by 1024?

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What's the remainder if 1022^1023 is divided by 1024?

There shouldn’t be a remainder. 1022 has one factor of two in it. 1024 is 2^10. 1022^1023 should have at least 10 2s in it (it will have 1023 factors of 2 in it) and therefore should be evenly divisible by 1024.

Bigger question though - what is the point of this question? I mean it, I don’t know why this question exists. I say that because I have little doubt that the person who asked it doesn’t know the answer to it. That makes this some kind of weird game. I see these questions now constantly. Some question where someone is trying to challenge people on their knowledge of the order of operations, or some sillily specific math question. And it’s rarely a math question that most people would have difficulty with, it’s just a math question that uses big numbers.

Answer 2

Answer:

Step-by-step explanation:

for example 2/3

so the remainder is -1 or 2 (2 divided by 3 is -1 or 2)

so actuall remainder is = divisor + remainder

hence we get (for convince let take -1)

=3+(-1)

=2

similarly

2023*2024*2025*2026/5

-2*-1*0*1

=0

so actual remainder is

5-0=5

so coming  to the sum

1021^1022/1023

=(-2)^1022/1023

=2^1022/1023

=2^1020*2^2/1023

=(2^10)^102 * 2^2 /1023

=1024^102*4/1023 ( 1024/1023=1 , 4/2023=4)

= 1*4

=4

here you go please understand step by step