What is the remainder when 3^21 + 9^21 + 27^21 + 81^21 is divided by 3^20+1 ?

3^21 can be represented as (3^20 + 1)3 - 3 Hence when complete term divided by (3^20 + 1) it will leave remainder of (-3) Similarly for other terms also remainder will be = -3, 9 , -27, 81 Hence adding all the remainders we will get final remainder as 60.

Take 3^20 = x
so question becomes remainder when 3x + 9 X^2 + 27x^3 + 81x^4 is divided by x+1
so remainder is 60

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