Consider a polynomial p(x) of any degree such that all its coefficients are positive integer valued. You can ask the value of p(x) for any two values of x. What values of x will you ask and can you find the exact polynomial using these values?
1st put x=1, get p(1), let p(1)=b, then put x=b=p(1).... then p(b) is nothing but the decimal conversion of base b number consisting of the integer coefficients of p(x)... here b is a valid base as b is greater than all the coeff. (as b = sum(all coeff.))... now extract all coeff. from p(b) just by converting from decimal to b-ary no.....
1st put x=1, get p(1), let p(1)=b, then put x=b=p(1).... then p(b) is nothing but the decimal conversion of base b number consisting of the integer coefficients of p(x)... here b is a valid base as b is greater than all the coeff. (as b = sum(all coeff.))... now extract all coeff. from p(b) just by converting from decimal to b-ary no.....
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