what is the remainder when 37^(n+2)+16^(n+1)+30^n is divided by 7
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Notation: N mod D = remainder when N is divided by D.
37^(n+2) mod 7 = (5*7 + 2)^(n+2) mod 7
= 2^(n+2) mod 7 = 4* 2^n mod 7
Similarly, 16^(n+1) mod 7 = (16 mod 7)^(n+1) mod 7
= 2^(n+1) mod 7 = 2* 2^n mod 7
30^n mod 7 = 2^n mod 7.
Answer = add the remainders of the terms and find remainder again.
Answer= (4+2+1)* 2^n mod 7
= 0
37^(n+2) mod 7 = (5*7 + 2)^(n+2) mod 7
= 2^(n+2) mod 7 = 4* 2^n mod 7
Similarly, 16^(n+1) mod 7 = (16 mod 7)^(n+1) mod 7
= 2^(n+1) mod 7 = 2* 2^n mod 7
30^n mod 7 = 2^n mod 7.
Answer = add the remainders of the terms and find remainder again.
Answer= (4+2+1)* 2^n mod 7
= 0
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