Finding remainder
Number Theory
Level
2
Find the remainder when 30^{99} + 61^{100} is divided by 31.
The answer is 0.
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30 = -1 (mod 31) or, 30^99= (-1)^99= -1 (mod 31) .......... (i) 61 = -1 (mod 31) , or , 61^100 = (-1)^100= 1 (mod 31) ................. (ii) Now , adding (i) & (ii) , we get, 30^99 + 61^100 = 0 (mod 31).