Welcome 2019 2019

Number Theory Level 3

For positive integer n n , f ( n ) = n m o d 3 f(n)=n \bmod 3 ,

f ( 201 7 2017 + 201 8 2018 + 201 9 2019 ) = ? f(2017^{2017}+2018^{2018}+2019^{2019})= ?

2 2 3 3 1 1 0 0

ابراهيم فقرا by ابراهيم فقرا , 23, Israel

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1 solution

Otto Bretscher
Dec 28, 2018

Modulo 3, the expression is 1 2017 + ( − 1 ) 2018 + 0 2019 ≡ 2 1^{2017}+(-1)^{2018}+0^{2019} \equiv \boxed{2}

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