Magic Hyperbeam - Qualification

Qualification

Qualifying the hyperbeam is less developed then it is on the magic hypercubes in fact only the k'th monagonal direction need to sum to:

S_k = m_k (_j=0∏n-1m_j - 1) / 2

for all k = 0..n-1 for the hyperbeam to be qualified {magic}

When the orders are not relatively prime the n-agonal sum can be restricted to:

S = lcm(m_i ; i = 0..n-1) (_j=0∏n-1m_j - 1) / 2

with all orders relatively prime this reaches its maximum:

S_max = _j=0∏n-1m_j (_j=0∏n-1m_j - 1) / 2