P880
projecteuler.net

Nested Radicals

ℹ️Published on Saturday, 2nd March 2024, 07:00 pm; Solved by 114;
Difficulty rating: 75%

(x,y) is called a nested radical pair if x and y are non-zero integers such that xy is not a cube of a rational number, and there exist integers a, b and c such that:

x3+y3=a3+b3+c3

For example, both (4,125) and (5,5324) are nested radical pairs:

43+1253=13+23+4353+53243=23+203+253

Let H(N) be the sum of |x|+|y| for all the nested radical pairs (x,y) where |x||y|N.
For example, H(103)=2535.

Find H(1015). Give your answer modulo 10313+2.



Soluzione

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