Problem 51471. Find integer solutions to an equation with a sum of binomial coefficients

Theorem 1 of chapter 27 of the book Diophantine Equations by Louis J. Mordell shows that the equation
y^2 = (x choose 0) + (x choose 1) + (x choose 2) + (x choose 3)
has a finite number of real, integer solutions (x,y). One of them has x = 7 because y^2 = 1 + 7 + 21 + 35 + 64 = 8^2.
Write a function that takes a value x = xmax­ and returns a two-column matrix with (x, y) pairs for x <= xmax. Sort the pairs in order of increasing x.

Solution Stats

30.43% Correct | 69.57% Incorrect
Last Solution submitted on Aug 11, 2021

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