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Computer Science Level 3

Find the sum of coefficients of the polynomial P ( x ) = ( 3 x 3 + x 2 + 5 x + 2 ) 16 P(x) = (3x^3 + x^2 + 5x + 2)^{16} when P ( x ) P(x) is expanded. Submit your answer in modulo 131.


The answer is 102.

Milan Milanic by Milan Milanic , 24, Serbia

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2 solutions

Soumava Pal
Feb 19, 2016

Put x=1 to get the sum of the coefficients. So we have (11**16)%131

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Bill Bell
Feb 18, 2016

I used sympy to expand the expression, then a regular expression to pick out most of the coefficients. Rather than writing a more complicated regular expression that would be able to find the purely numerical coefficient as well as the others, and knowing that it would be presented at the end, I dug it out using the string method rfind . 

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from sympy import *
from re import compile

coeffRE=compile('([0-9]+)\*')

var('x')
expr=str(((3*x**3+x**2+5*x+2)**16).expand())

total=sum([int(piece) for piece in coeffRE.findall(expr)])
total+=int(expr[1+expr.rfind(' '):])

print (total%131)

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