LIGHT MATRICES OF PRIME DETERMINANT.

For A = (ai,j ) a square integer matrix of prime determinant p, set w(A) =∑ i,j ǀai,j ǀ . We are interested in the smallest possible value wp for w(A), and we show that lim p→∞wp/ log2(p) = 5/2. We also show that wp ⩽ 2.5 log2(p) if and only if p = 2, 7, 13, 37 or a Fermat prime. Our results can also be interpreted as being about addition chains or about presentations of finite cyclic groups. [ABSTRACT FROM AUTHOR]