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Solved Homework 2 CSCI 301 1) [4 points] Prove that 9 | (4#$ + 8) for every integer 𝑛 β‰₯ 0. 2) [4 points] Prove that βˆ‘ (8𝑖 βˆ’ 5) $

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1) [4 points] Prove that 9 | (4#$ + 8) for every integer 𝑛 β‰₯ 0.
2) [4 points] Prove that βˆ‘ (8𝑖 βˆ’ 5) $
/01 = 4𝑛3 βˆ’ 𝑛 for every positive integer n.
3) [4 points] Prove that 13 + 23 + 33 + 43 + β‹― + 𝑛3 = $($91)(3$91)
: for every positive
integer n.