let-P-x-is-polinomial-with-integer-coefficient-s-t-P-6-P-38-P-57-19-is-divided-by-114-P-13-479-and-P-0-what-is-minimum-value-of-P-0-

Tinku Tara June 4, 2023 Number Theory 0 Comments

Question Number 192909 by uchihayahia last updated on 30/May/23

let P(x) is polinomial with integer coefficient s.t P(6)P(38)P(57)+19 is divided by 114. P(-13)=479 and P≥0 what is minimum value of P(0)?

$$\: \\ $$$$\:{let}\:{P}\left({x}\right)\:{is}\:{polinomial}\:{with}\:{integer} \\ $$$$\:{coefficient}\:{s}.{t}\:{P}\left(\mathrm{6}\right){P}\left(\mathrm{38}\right){P}\left(\mathrm{57}\right)+\mathrm{19}\:{is} \\ $$$$\:{divided}\:{by}\:\mathrm{114}.\:{P}\left(-\mathrm{13}\right)=\mathrm{479}\:{and}\:{P}\geqslant\mathrm{0} \\ $$$$\:{what}\:{is}\:{minimum}\:{value}\:{of}\:{P}\left(\mathrm{0}\right)? \\ $$$$ \\ $$

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let-P-x-is-polinomial-with-integer-coefficient-s-t-P-6-P-38-P-57-19-is-divided-by-114-P-13-479-and-P-0-what-is-minimum-value-of-P-0-

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