Table of Contents
Problem
Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:
Triangle Tn=n(n+1)/2 1, 3, 6, 10, 15, … Pentagonal Pn=n(3n−1)/2 1, 5, 12, 22, 35, … Hexagonal Hn=n(2n−1) 1, 6, 15, 28, 45, … It can be verified that T285 = P165 = H143 = 40755.
Find the next triangle number that is also pentagonal and hexagonal.
Solution
简单,一元二次方程组.
Answer
1533776805
Source:project-euler