Question

यदी 7^21+7^22+7^23+7^24 को 25 से विभाजित किया जाये तो शेष क्या बचेगा?​

Answer 1

Answer:

What is the remainder when 7^21+7^22+7^23+7^24 is divided by 25?

For n∈N∪{0} ,

f(n)=7n+7n+1+7n+2+7n+3

=7n(1+72)+7n+1(1+72)

=7n(1+7)(1+72)

is a multiple of 1+72=50 . Hence the remainder when f(n) is divided by 25 is 0 for each n∈N∪{0} . ■

To find out remainder we use congruence module 25.

Note that 7^2=49 =-1(mod 25), using this we have

7^21 = (7^2)^10 * 7 = 7 (mod 25) as (7^2)^10 = 1

Similarly we have 7^22= -1 (mod 25), 7^23= -7 (mkd25), 7^24 =1 ( mod 25)

So remainder is 7-1–7+1 =0

Hence answer is 0

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Answer 2

Answer:

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Step-by-step explanation:

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