Don't do the polynomial

Number Theory Level 3

Given that $f(x)=1337x^{2015}-64x^{19}+413x^2-1729x+100,$ find $f(2017)\text{ mod }8.$

5 1 3 7

1 solution

Kazem Sepehrinia
Jul 2, 2015

Note that $2017\stackrel{8}{\equiv} 1$ so $2017^n\stackrel{8}{\equiv} 1$ for $n \ge 0$ , hence $f(2017)\stackrel{8}{\equiv} 1337-64+413-1729+100\stackrel{8}{\equiv} 57 \stackrel{8}{\equiv} 1$

Don't do the polynomial

1 solution

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