The first test case is wrong 0 and 21 are triangular numbers too (https://oeis.org/A000217), therefore:
[ 0, 6;
PS: And 0 does not make a pair with every number in this case.
What's wrong with the case x=20 in test suite? Why is y_correct=[ 10 10] ? I cannot pass it.
I don't know why your cheat isn't working, but look closely at what numbers your "for n=1:N" loop generates for that case.
Make the vector [1 2 3 4 5 6 7 8 9 10]
Length of a short side
Narcissistic number ?
A (wrong) place for everything, and everything in its (wrong) place
Points on a Sphere
Three...is a magic number.
Diophantine Equations (Inspired by Project Euler, problem 66)
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